SOLUTION: A manufacturer sells a product at $8.80 per unit, selling all produced. The fixed cost is $2,160 and the variable cost is $7.25 per unit. (a) At what level of production will ther

Question 215241This question is from textbook Applied Calculus
: A manufacturer sells a product at $8.80 per unit, selling all produced. The fixed cost is $2,160 and the variable cost is $7.25 per unit.
(a) At what level of production will there be a profit of $4,100?
(b) At what level of production will there be a loss of $1,200?
(c) At what level of production will the break-even point occur? This question is from textbook Applied Calculus

Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
A manufacturer sells a product at $8.80 per unit, selling all produced. The fixed cost is $2,160 and the variable cost is $7.25 per unit.
.
Profit equation:
P(x) = 8.80x - 7.25x - 2160
P(x) = 1.55x - 2160
where
x is the number of units
.
(a) At what level of production will there be a profit of $4,100?
Set P(x) = 4100 and solve for x:
4100 = 1.55x - 2160
6260 = 1.55x
4038.71 units = x
.
(b) At what level of production will there be a loss of $1,200?
Set P(x) = -1200 and solve for x:
-1200 = 1.55x - 2160
960 = 1.55x
619.35 units = x
.
(c) At what level of production will the break-even point occur?
Set P(x) = 0 and solve for x:
0 = 1.55x - 2160
2160 = 1.55x
1393.55 units = x
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