M I M E 3 1 0 E N G I N E E R I N G E C O N O M YSOLUTIONS TO PROBLEM SET #4 – PRODUCTION AND COST ANALYSES1.The recovery method with the highest unit profit (revenue less cost) is preferred. ProcessB has a higher recovery than process A, but it also has a higher cost. Thus, a tradeoff existsbetween the two processes. The economic value of the higher recovery is a function of the valueof recovered metal. At low values of the metal, process A, with the lower cost, is preferred.However, for high values of the metal, process B is preferred, because the value of recoveringmore metal outweighs the higher cost of the process. For one tonne of mine product containingan amount of metal M, the profit is given by:M • Recovery (Unit revenue - Unit cost)Unit profit for process A: 0.75 M (6.00 - 3.00) = 2.25 MUnit profit for process B: 0.8 M (6.00 - 3.25) = 2.2 MAt a unit metal value of $6.00 per tonne, process A has the highest unit profit, and it is thereforepreferred.Let v be the unit metal value. Process B is more economical when:(ProfitB- ProfitA) > 0ProfitB- ProfitA= [0.8 M (v - 3.25)] - [0.75 M (v - 3)] = M [0.05 v - 0.35]Therefore, process B is preferred whenM [0.05 v - 0.35] > 0or whenv > 7The recovery method should be changed from A to B when the value of the metal exceeds$7/tonne.2.The total cost function is linear because the unit variable costs are constant within theplant's range of operating capacities.i)Let Q represent the production rate. At the break-even rate (Q*), total revenue equalstotal costs.TR = p • Q = 500 QTC = FC + VC = FC + vc • Q = 15 000 + 320 Q26
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