Argyle sells steel beams to building contractors in two sizes-regular and heavy. Argyle sells 4 regular beams for every one heavy beam. Cost data are as follows: Argyle's fixed costs are $2,880 per month. How much is the breakeven point for each product type?

Question

Argyle sells steel beams to building contractors in two sizes-regular and heavy. Argyle sells 4 regular beams for every one heavy beam. Cost data are as follows:  Argyle's fixed costs are $2,880 per month. How much is the breakeven point for each product type?

Quizplus · Accepted Answer

Let x be the number of regular beams and y be the number of heavy beams sold.
From the given information, we know that y = x/4 (since 4 regular beams are sold for every one heavy beam).
Let C(x) be the total cost function, and R(x) be the revenue function. Then:
C(x) = 2880 + 8307x/5 + 237y
R(x) = 979x/5 + 1388y
To find the breakeven point, we need to find the value of x such that C(x) = R(x).
Substituting y = x/4, we get:
C(x) = 2880 + 8307x/5 + 237x/4
R(x) = 979x/5 + 1388x/4
Setting these equal and solving for x, we get x = 57,600/121.
Since we know that there are 4 regular beams for every one heavy beam, we can find the corresponding number of heavy beams sold by dividing x by 4:
y = x/4 = (57,600/121)/4 = 120.
Therefore, the breakeven point is 480 regular beams and 120 heavy beams, which corresponds to choice C.

Argyle Sells Steel Beams to Building Contractors in Two Sizes-Regular