Suggested answers with workings:
Solution for a:
Fundamentally, profit maximization is achieved when dTC/dx = dTR/dx (or when MC = MR). Therefore, it is advisable to calculate the marginal cost (MC) and the fixed costs (FC) first, so that we can use them to form the total cost (TC) function later. On the other hand, total revenue (TR) function can be found by multiplying selling price (SP) per unit with the output quantity. To solve ‘question a’, we need to calculate what is the maximum profit when the new machine is not leased and when the new machine is leased. Decision on whether to lease or not to lease the machine will depend on the option that can give a higher profit.
Again, this is quite similar with ‘question a’. Profit maximization is achieved when dTC/dx = dTR/dx (or when MR = MC).
Solution of b(ii):
Please bear in mind that, profit maximization ≠ sales maximization. Total revenue will be maximized when MR=0.