{"id":2411,"date":"2020-08-05T17:10:38","date_gmt":"2020-08-05T21:10:38","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/chbe220\/?post_type=chapter&p=2411"},"modified":"2020-08-12T16:15:51","modified_gmt":"2020-08-12T20:15:51","slug":"practice-exercises-2","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/chbe220\/chapter\/practice-exercises-2\/","title":{"raw":"Practice Exercises","rendered":"Practice Exercises"},"content":{"raw":"

Multiple Choice Questions<\/h2>\r\n
\r\n

Exercise: Equipment Prices with the Effect of Capacity and Time<\/p>\r\n\r\n<\/header>\r\n

\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Equipment Type<\/th>\r\nRange of Correlation<\/th>\r\nCapacity Units<\/th>\r\nCost Exponent (n)<\/th>\r\n<\/tr>\r\n
Air compressor, multiple stages<\/td>\r\n1 -1500<\/td>\r\n[latex]kW[\/latex]<\/td>\r\n0.85<\/td>\r\n<\/tr>\r\n
Shell and tube heat exchanger stainless steel<\/td>\r\n1.9 \u2013 1860<\/td>\r\n[latex]m^2[\/latex]<\/td>\r\n0.60<\/td>\r\n<\/tr>\r\n
Horizontal tank carbon steel<\/td>\r\n0.5-74<\/td>\r\n[latex]m^3[\/latex]<\/td>\r\n0.30<\/td>\r\n<\/tr>\r\n
centrifugal pump stainless steel<\/td>\r\n1-70<\/td>\r\n[latex]hp[\/latex]<\/td>\r\n0.67<\/td>\r\n<\/tr>\r\n
Crystalizer<\/td>\r\n0.2-3.8<\/td>\r\n[latex]m^3[\/latex]<\/td>\r\n0.47<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Year<\/th>\r\nMarshall and Swift Equipment cost index<\/th>\r\nChemical Engineering Plant Cost Index<\/th>\r\n<\/tr>\r\n
1996<\/td>\r\n211.7<\/td>\r\n154.7<\/td>\r\n<\/tr>\r\n
2000<\/td>\r\n264.8<\/td>\r\n169.3<\/td>\r\n<\/tr>\r\n
2004<\/td>\r\n301.7<\/td>\r\n186.3<\/td>\r\n<\/tr>\r\n
2008<\/td>\r\n339.2<\/td>\r\n212.8<\/td>\r\n<\/tr>\r\n
2012<\/td>\r\n391.5<\/td>\r\n227.8<\/td>\r\n<\/tr>\r\n
2016<\/td>\r\n418.9<\/td>\r\n237.8<\/td>\r\n<\/tr>\r\n
2020<\/td>\r\n458.3<\/td>\r\n258.8<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nIn 2008, a carbon steel horizontal tank with a capacity of 26.5[latex]m^3[\/latex] gallons costs $6700, then which of the following is the closest estimation to the cost of the same type of tank with a capacity of 50[latex]m^3[\/latex] cost in 2020?\r\n\r\na)$9800\r\n\r\nb)$10,100\r\n\r\nc)$7,500\r\n\r\nd)$8,000\r\n\r\n<\/div>\r\n<\/div>\r\n
\r\n

Solution<\/h3>\r\nb) $10,100<\/strong>\r\n\r\nWe combine the effect of capacity and time by multiplying the two factors. For time, we use the Marshall and Swift Equipment cost index because we are interested in the cost of a piece of equipment.\r\n\r\n\\begin{align*}\r\nC_{2} &=C_{1}\u00d7\\Big(\\frac{A_{a}}{A_{b}}\\Big)^n\u00d7\\Big(\\frac{I_{2}}{I_{1}}\\Big)\\\\\r\nC_{2} & = $6700\u00d7\\Big(\\frac{50}{26.5}\\Big)^{0.30}\u00d7\\Big(\\frac{458.3}{339.2}\\Big)\\\\\r\nC_{2} & \u2248 $10,100\r\n\\end{align*}\r\n\r\n<\/div>\r\n
\r\n

Exercise: Preliminary Estimation of Purchased Equipment Costs<\/p>\r\n\r\n<\/header>\r\n

\r\n\r\nUsing the preliminary estimation of purchased equipment costs, estimate the price of a centrifugal compressor with the power of 400kW.\r\n\r\nThe value of a, b and n are shown as follows:\r\n\r\n\r\n\r\n\r\n
Equipment<\/td>\r\nUnits for Size, S<\/td>\r\nS lower<\/td>\r\nS upper<\/td>\r\na<\/td>\r\nb<\/td>\r\nn<\/td>\r\n<\/tr>\r\n
centrifugal compressors<\/td>\r\ndriver power, kW<\/td>\r\n75<\/td>\r\n30,000<\/td>\r\n490,000<\/td>\r\n16,800<\/td>\r\n0.6<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\na) $1,100,000\r\n\r\nb) $7,210,000\r\n\r\nc) $490,000\r\n\r\nd) the size of the equipment is out of the range for effective estimation\r\n\r\n<\/div>\r\n<\/div>\r\n
\r\n

Solution<\/h3>\r\na) $1,100,000<\/strong>\r\n\r\nThe size of the compressor is 400kW, which is within the range of S lower and S upper, so we can eliminate choice d).\r\nThen we can use the formula:\r\n\r\n\\begin{align*}\r\nC_e&=a+bS^n\\\\\r\n&=490,000+16,800\u00d7(400)^{0.6}\\\\\r\n&\u2248 $1,100,000\r\n\\end{align*}\r\n\r\n<\/div>\r\n \r\n
\r\n

Exercise: Calculating Depreciation<\/p>\r\n\r\n<\/header>\r\n

\r\n\r\n\r\n\r\n\r\n\r\n\r\n
<\/td>\r\nEquipment A<\/td>\r\nEquipment B<\/td>\r\n<\/tr>\r\n
Purchased Value<\/td>\r\n$80,000<\/td>\r\n$100,000<\/td>\r\n<\/tr>\r\n
Salvage Value<\/td>\r\n$30,000<\/td>\r\n$40,000<\/td>\r\n<\/tr>\r\n
Life of Equipment<\/td>\r\n5 years<\/td>\r\n10 years<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nSuppose we have 2 choices for a piece of equipment that serves the same purpose in our process, and we want to choose the equipment with the smallest depreciation, which one should we choose?\r\n\r\na) equipment A\r\n\r\nb) equipment B\r\n\r\nc)\u00a0 they have the same depreciation value\r\n\r\n<\/div>\r\n<\/div>\r\n
\r\n

Solution<\/h3>\r\nb) equipment B<\/strong>\r\n\r\n\\begin{align*}\r\n&\\text{Depreciation of equipment A}\\\\\r\n&=\\frac{\\text{purchased value}-\\text{salvage value}}{\\text{life of equipment }(n)}\\\\\r\n&=\\frac{$80,000-$30,000}{5years}\\\\\r\n&=$10000\/year\r\n\\end{align*}\r\n\r\n\\begin{align*}\r\n&\\text{Depreciation of equipment B}\\\\\r\n&=\\frac{\\text{purchased value}-\\text{salvage value}}{\\text{life of equipment }(n)}\\\\\r\n&=\\frac{$100,000-$40,000}{10years}\\\\\r\n&=$6000\/year\r\n\\end{align*}\r\n\r\n<\/div>\r\n \r\n

Long Answer Questions<\/h2>\r\n
\r\n

Exercise: Estimating Project Cost Using the Lang Factor<\/p>\r\n\r\n<\/header>\r\n

\r\n\r\n\"\"\r\n\r\nShown above is the block flow diagram of a carbon-capture process. The cost of equipment for each step is listed as follows:\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Equipment<\/strong><\/td>\r\nPrice<\/strong><\/td>\r\n<\/tr>\r\n
Absorber<\/td>\r\n$80,000<\/td>\r\n<\/tr>\r\n
Heat Exchanger<\/td>\r\n$65,000<\/td>\r\n<\/tr>\r\n
Stripper<\/td>\r\n$50,000<\/td>\r\n<\/tr>\r\n
5-stage Compression<\/td>\r\n$120,000<\/td>\r\n<\/tr>\r\n
Separator<\/td>\r\n$30,000<\/td>\r\n<\/tr>\r\n
Mixer<\/td>\r\n$30,000<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n \r\n\r\n\r\n\r\n\r\n\r\n\r\n
Type of Plant<\/strong><\/td>\r\nFCI<\/strong><\/td>\r\nTCI<\/strong><\/td>\r\n<\/tr>\r\n
solid processing plant<\/td>\r\n3.9<\/td>\r\n4.6<\/td>\r\n<\/tr>\r\n
solid-fluid processing plant<\/td>\r\n4.1<\/td>\r\n4.9<\/td>\r\n<\/tr>\r\n
fluid processing plant<\/td>\r\n4.8<\/td>\r\n5.7<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nAll of the compounds are in liquid or vapour states. Estimate the TCI of the project.\r\n\r\n<\/div>\r\n<\/div>\r\n
\r\n

Solution<\/h3>\r\nSince all of the compounds are in liquid or vapour states, we take [latex]F_{lang}=5.7[\/latex]\r\n\r\n\\begin{align*}\r\nC_{TM}&=F_{lang} \\sum_{i=1}^{n}C_{p,i}\\\\\r\n&=5.7\u00d7($80,000+$65,000+$50,000+$120,000\\\\\r\n&\\;\\;\\;\\;\\;\\;+$30,000+$30,000)\\\\\r\n&=$2,137,500\r\n\\end{align*}\r\n\r\n<\/div>\r\n
\r\n

Exercise: Calculating the number of Operating Labour<\/p>\r\n\r\n<\/header>\r\n

\r\n\r\nShown below is a PFD of a catalytic reforming plant used in oil refineries to produce a high-octane gasoline component. Calculate the number of operators needed per shift for the process.\r\n\r\n\"\"\r\n

Image obtained from User: mbeychok via Wikimedia Commons<\/a> \/ CC BY-SA 3.0<\/p>\r\nNote: Naphtha is a flammable liquid<\/strong> hydrocarbon mixture\r\n\r\n<\/div>\r\n<\/div>\r\n

\r\n

Solution<\/h3>\r\nFrom the labels, the process does not involve handling solids([latex]P=0[\/latex]). And we can count that we have a total of 12 process steps that handle fluids without accounting for the number of pumps and vessels, shown in the diagram below:\r\n\r\n\"\"\r\n\r\nSo [latex]P=0\\;;N_{np}=12[\/latex]. Substitute this into the formula:\r\n\r\n\\begin{align*}\r\nN_{OL}&=(6.29+31.7\u00d7(0)^2+0.23\u00d712)^{0.5}\\\\\r\n& = 3.008\\\\\r\n& \u2248 4\r\n\\end{align*}\r\n\r\nThe number of operating labour is rounded up to the nearest integer.\r\n\r\n<\/div>\r\n \r\n
\r\n

Exercise: Return on Investment<\/p>\r\n\r\n<\/header>\r\n

\r\n\r\nSuppose the estimation of the key manufacturing costs for our process are listed below:\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
[latex]FCI[\/latex]<\/td>\r\n$1,650,000<\/td>\r\n<\/tr>\r\n
[latex] TCI[\/latex]<\/td>\r\n$2,000,000<\/td>\r\n<\/tr>\r\n
[latex]C_{RM}[\/latex]<\/td>\r\n$600,000<\/td>\r\n<\/tr>\r\n
[latex]C_{UT}[\/latex]<\/td>\r\n$280,000<\/td>\r\n<\/tr>\r\n
[latex]C_{OL}[\/latex]<\/td>\r\n$320,000<\/td>\r\n<\/tr>\r\n
[latex]C_{WT}[\/latex]<\/td>\r\n$500,000<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\na) Calculate the cost of manufacturing (do not include depreciation)\r\n\r\nb) If the market price of the product is $500\/tonne, how many tonnes of the product do we need to sell per year to get an ROI of 10%?\r\n\r\n<\/div>\r\n<\/div>\r\n
\r\n

Solution<\/h3>\r\na)\r\n\\begin{align*}\r\nCOM&=0.180FCI+1.23(C_{RM}+C_{WT}+C_{UT})+2.73C_{OL}\\\\\r\n&=0.180\u00d7$1,650,000+1.23\u00d7($600,000+$500,000+$280,000)\\\\\r\n&\\;\\;\\;\\;\\;\\;+2.73\u00d7$320,000\\\\\r\n&=$2,868,000\r\n\\end{align*}\r\n\r\nb)\r\n\r\n\\begin{align*}\r\nROI&=\\frac{revenue-COM}{TCI}\u00d7100\\text{%}\\\\\r\nROI\u00d7TCI&=revenue-COM\\\\\r\nrevenue&=ROI\u00d7TCI+COM\\\\\r\nrevenue&=10\\text{%}\u00d7$2,000,000+$2,868,000\\\\\r\nrevenue&=$3,068,000\r\n\\end{align*}\r\n\r\n \r\n\r\n\\begin{align*}\r\nrevenue&=unit\\;price\\;of\\;product\u00d7sales\\\\\r\nsales&=\\frac{revenue}{unit\\;price\\;of\\;product}\\\\\r\nsales&=\\frac{$3,068,000}{$500\/tonnes}\\\\\r\nsales&=6136\\;tonnes\r\n\\end{align*}\r\n\r\n<\/div>\r\n ","rendered":"

Multiple Choice Questions<\/h2>\n
\n
\n

Exercise: Equipment Prices with the Effect of Capacity and Time<\/p>\n<\/header>\n

\n\n\n\n\n\n\n\n\n
Equipment Type<\/th>\nRange of Correlation<\/th>\nCapacity Units<\/th>\nCost Exponent (n)<\/th>\n<\/tr>\n
Air compressor, multiple stages<\/td>\n1 -1500<\/td>\n[latex]kW[\/latex]<\/td>\n0.85<\/td>\n<\/tr>\n
Shell and tube heat exchanger stainless steel<\/td>\n1.9 \u2013 1860<\/td>\n[latex]m^2[\/latex]<\/td>\n0.60<\/td>\n<\/tr>\n
Horizontal tank carbon steel<\/td>\n0.5-74<\/td>\n[latex]m^3[\/latex]<\/td>\n0.30<\/td>\n<\/tr>\n
centrifugal pump stainless steel<\/td>\n1-70<\/td>\n[latex]hp[\/latex]<\/td>\n0.67<\/td>\n<\/tr>\n
Crystalizer<\/td>\n0.2-3.8<\/td>\n[latex]m^3[\/latex]<\/td>\n0.47<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n\n\n\n\n\n\n\n\n
Year<\/th>\nMarshall and Swift Equipment cost index<\/th>\nChemical Engineering Plant Cost Index<\/th>\n<\/tr>\n
1996<\/td>\n211.7<\/td>\n154.7<\/td>\n<\/tr>\n
2000<\/td>\n264.8<\/td>\n169.3<\/td>\n<\/tr>\n
2004<\/td>\n301.7<\/td>\n186.3<\/td>\n<\/tr>\n
2008<\/td>\n339.2<\/td>\n212.8<\/td>\n<\/tr>\n
2012<\/td>\n391.5<\/td>\n227.8<\/td>\n<\/tr>\n
2016<\/td>\n418.9<\/td>\n237.8<\/td>\n<\/tr>\n
2020<\/td>\n458.3<\/td>\n258.8<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

In 2008, a carbon steel horizontal tank with a capacity of 26.5[latex]m^3[\/latex] gallons costs $6700, then which of the following is the closest estimation to the cost of the same type of tank with a capacity of 50[latex]m^3[\/latex] cost in 2020?<\/p>\n

a)$9800<\/p>\n

b)$10,100<\/p>\n

c)$7,500<\/p>\n

d)$8,000<\/p>\n<\/div>\n<\/div>\n

\n

Solution<\/h3>\n

b) $10,100<\/strong><\/p>\n

We combine the effect of capacity and time by multiplying the two factors. For time, we use the Marshall and Swift Equipment cost index because we are interested in the cost of a piece of equipment.<\/p>\n

\\begin{align*}
\nC_{2} &=C_{1}\u00d7\\Big(\\frac{A_{a}}{A_{b}}\\Big)^n\u00d7\\Big(\\frac{I_{2}}{I_{1}}\\Big)\\\\
\nC_{2} & = $6700\u00d7\\Big(\\frac{50}{26.5}\\Big)^{0.30}\u00d7\\Big(\\frac{458.3}{339.2}\\Big)\\\\
\nC_{2} & \u2248 $10,100
\n\\end{align*}<\/p>\n<\/div>\n

\n
\n

Exercise: Preliminary Estimation of Purchased Equipment Costs<\/p>\n<\/header>\n

\n

Using the preliminary estimation of purchased equipment costs, estimate the price of a centrifugal compressor with the power of 400kW.<\/p>\n

The value of a, b and n are shown as follows:<\/p>\n\n\n\n\n
Equipment<\/td>\nUnits for Size, S<\/td>\nS lower<\/td>\nS upper<\/td>\na<\/td>\nb<\/td>\nn<\/td>\n<\/tr>\n
centrifugal compressors<\/td>\ndriver power, kW<\/td>\n75<\/td>\n30,000<\/td>\n490,000<\/td>\n16,800<\/td>\n0.6<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

a) $1,100,000<\/p>\n

b) $7,210,000<\/p>\n

c) $490,000<\/p>\n

d) the size of the equipment is out of the range for effective estimation<\/p>\n<\/div>\n<\/div>\n

\n

Solution<\/h3>\n

a) $1,100,000<\/strong><\/p>\n

The size of the compressor is 400kW, which is within the range of S lower and S upper, so we can eliminate choice d).
\nThen we can use the formula:<\/p>\n

\\begin{align*}
\nC_e&=a+bS^n\\\\
\n&=490,000+16,800\u00d7(400)^{0.6}\\\\
\n&\u2248 $1,100,000
\n\\end{align*}<\/p>\n<\/div>\n

 <\/p>\n

\n
\n

Exercise: Calculating Depreciation<\/p>\n<\/header>\n

\n\n\n\n\n\n\n
<\/td>\nEquipment A<\/td>\nEquipment B<\/td>\n<\/tr>\n
Purchased Value<\/td>\n$80,000<\/td>\n$100,000<\/td>\n<\/tr>\n
Salvage Value<\/td>\n$30,000<\/td>\n$40,000<\/td>\n<\/tr>\n
Life of Equipment<\/td>\n5 years<\/td>\n10 years<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Suppose we have 2 choices for a piece of equipment that serves the same purpose in our process, and we want to choose the equipment with the smallest depreciation, which one should we choose?<\/p>\n

a) equipment A<\/p>\n

b) equipment B<\/p>\n

c)\u00a0 they have the same depreciation value<\/p>\n<\/div>\n<\/div>\n

\n

Solution<\/h3>\n

b) equipment B<\/strong><\/p>\n

\\begin{align*}
\n&\\text{Depreciation of equipment A}\\\\
\n&=\\frac{\\text{purchased value}-\\text{salvage value}}{\\text{life of equipment }(n)}\\\\
\n&=\\frac{$80,000-$30,000}{5years}\\\\
\n&=$10000\/year
\n\\end{align*}<\/p>\n

\\begin{align*}
\n&\\text{Depreciation of equipment B}\\\\
\n&=\\frac{\\text{purchased value}-\\text{salvage value}}{\\text{life of equipment }(n)}\\\\
\n&=\\frac{$100,000-$40,000}{10years}\\\\
\n&=$6000\/year
\n\\end{align*}<\/p>\n<\/div>\n

 <\/p>\n

Long Answer Questions<\/h2>\n
\n
\n

Exercise: Estimating Project Cost Using the Lang Factor<\/p>\n<\/header>\n

\n

\"\"<\/p>\n

Shown above is the block flow diagram of a carbon-capture process. The cost of equipment for each step is listed as follows:<\/p>\n\n\n\n\n\n\n\n\n\n
Equipment<\/strong><\/td>\nPrice<\/strong><\/td>\n<\/tr>\n
Absorber<\/td>\n$80,000<\/td>\n<\/tr>\n
Heat Exchanger<\/td>\n$65,000<\/td>\n<\/tr>\n
Stripper<\/td>\n$50,000<\/td>\n<\/tr>\n
5-stage Compression<\/td>\n$120,000<\/td>\n<\/tr>\n
Separator<\/td>\n$30,000<\/td>\n<\/tr>\n
Mixer<\/td>\n$30,000<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

 <\/p>\n\n\n\n\n\n\n
Type of Plant<\/strong><\/td>\nFCI<\/strong><\/td>\nTCI<\/strong><\/td>\n<\/tr>\n
solid processing plant<\/td>\n3.9<\/td>\n4.6<\/td>\n<\/tr>\n
solid-fluid processing plant<\/td>\n4.1<\/td>\n4.9<\/td>\n<\/tr>\n
fluid processing plant<\/td>\n4.8<\/td>\n5.7<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

All of the compounds are in liquid or vapour states. Estimate the TCI of the project.<\/p>\n<\/div>\n<\/div>\n

\n

Solution<\/h3>\n

Since all of the compounds are in liquid or vapour states, we take [latex]F_{lang}=5.7[\/latex]<\/p>\n

\\begin{align*}
\nC_{TM}&=F_{lang} \\sum_{i=1}^{n}C_{p,i}\\\\
\n&=5.7\u00d7($80,000+$65,000+$50,000+$120,000\\\\
\n&\\;\\;\\;\\;\\;\\;+$30,000+$30,000)\\\\
\n&=$2,137,500
\n\\end{align*}<\/p>\n<\/div>\n

\n
\n

Exercise: Calculating the number of Operating Labour<\/p>\n<\/header>\n

\n

Shown below is a PFD of a catalytic reforming plant used in oil refineries to produce a high-octane gasoline component. Calculate the number of operators needed per shift for the process.<\/p>\n

\"\"<\/p>\n

Image obtained from User: mbeychok via Wikimedia Commons<\/a> \/ CC BY-SA 3.0<\/p>\n

Note: Naphtha is a flammable liquid<\/strong> hydrocarbon mixture<\/p>\n<\/div>\n<\/div>\n

\n

Solution<\/h3>\n

From the labels, the process does not involve handling solids([latex]P=0[\/latex]). And we can count that we have a total of 12 process steps that handle fluids without accounting for the number of pumps and vessels, shown in the diagram below:<\/p>\n

\"\"<\/p>\n

So [latex]P=0\\;;N_{np}=12[\/latex]. Substitute this into the formula:<\/p>\n

\\begin{align*}
\nN_{OL}&=(6.29+31.7\u00d7(0)^2+0.23\u00d712)^{0.5}\\\\
\n& = 3.008\\\\
\n& \u2248 4
\n\\end{align*}<\/p>\n

The number of operating labour is rounded up to the nearest integer.<\/p>\n<\/div>\n

 <\/p>\n

\n
\n

Exercise: Return on Investment<\/p>\n<\/header>\n

\n

Suppose the estimation of the key manufacturing costs for our process are listed below:<\/p>\n\n\n\n\n\n\n\n\n
[latex]FCI[\/latex]<\/td>\n$1,650,000<\/td>\n<\/tr>\n
[latex]TCI[\/latex]<\/td>\n$2,000,000<\/td>\n<\/tr>\n
[latex]C_{RM}[\/latex]<\/td>\n$600,000<\/td>\n<\/tr>\n
[latex]C_{UT}[\/latex]<\/td>\n$280,000<\/td>\n<\/tr>\n
[latex]C_{OL}[\/latex]<\/td>\n$320,000<\/td>\n<\/tr>\n
[latex]C_{WT}[\/latex]<\/td>\n$500,000<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

a) Calculate the cost of manufacturing (do not include depreciation)<\/p>\n

b) If the market price of the product is $500\/tonne, how many tonnes of the product do we need to sell per year to get an ROI of 10%?<\/p>\n<\/div>\n<\/div>\n

\n

Solution<\/h3>\n

a)
\n\\begin{align*}
\nCOM&=0.180FCI+1.23(C_{RM}+C_{WT}+C_{UT})+2.73C_{OL}\\\\
\n&=0.180\u00d7$1,650,000+1.23\u00d7($600,000+$500,000+$280,000)\\\\
\n&\\;\\;\\;\\;\\;\\;+2.73\u00d7$320,000\\\\
\n&=$2,868,000
\n\\end{align*}<\/p>\n

b)<\/p>\n

\\begin{align*}
\nROI&=\\frac{revenue-COM}{TCI}\u00d7100\\text{%}\\\\
\nROI\u00d7TCI&=revenue-COM\\\\
\nrevenue&=ROI\u00d7TCI+COM\\\\
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