A small firm intends to increase the capacity of a bottleneck operation by addin

Question

A small firm intends to increase the capacity of a bottleneck operation by adding a new machine. Two alternatives, A & B, have been identified, and the associated costs and revenue have been estimated. Annual fixed costs would be $12600 for A and $ 25200 for B; Variable cost per unit would be $ 10.8 for A and $ 7.2 for B; and revenue per unit would be $ 18.4.

a.       Determine each alternatives breakeven point in units? ( 5 points)

b.      At what volume of output would the two alternatives yield the same profit? (10 points)

c.       If the expected demand is 4000 units, which alternative would yield the higher profit? (5 points)

?

Explanation / Answer

a)

alternative A::

At break even point, profit is zero. Therefore, revenue and costs have to be equal

Let n be the number of breakeven units

n*18.4 = 12600+10.8*n

n = 1657.895 units

Alternative B::

Let m be the number of break even units

25200+7.2*m = 18.4*m

m= 2250 units

b)

Let volume be v

12600+10.8*v = 25200+7.2*v

v= 3500 units

c)

Profit of A = 4000*18.4-12600- 10.8*4000 = $17800

Profit of B = 4000*18.4 - 25200 - 7.2*4000 = $19600

Alternative B would yield higher profit

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