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A manufacturing firm is considering the following capacity planning approach in the production of their new product. Each machine can produce only 2000 units/year, and the firm can buy up to 2 machines (we assume that all machines are identical). The selling price of each unit of the product is $30/unit. In order to produce one unit of the product, the variable cost is $20/unit. Fixed investment costs indicated for 2 machines is not the incremental cost, but the total fixed investment cost. For example, 2-machine has a total fixed cost of $12,000/yr, not $20,000.
Output Range/year
Fixed Cost/year
0-2000 (1 machine)
$8,000
2001-4000 (2 machines)
$12,000
a. If the firm buys one machine, then determine the break-even point.
b. If the firm buys two machines, then determine the break-even point.
c. Suppose that the excess demand can be lost without any penalty. Determine all possible production volumes in the range of (1000, 4000] such that it is optimal to buy two machines.
d. What volume of output will be required to achieve a profit of $16,000 if the optimal capacity decision is made?
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