Question

The unit cost, in dollars, to produce bins of cat food is $4 and the fixed cost is $18424. The revenue function, in dollars, is R(x)=−2x^2+478x
Find the cost function.
C(x)=
Find the profit function.
P(x)=
At what quantity is the smallest break-even point?

Answer 1

Answer:

49

Step-by-step explanation:

The cost function is the sum of the costs as a function of the number of bins made.

C(x) = 4x + 18424

The profit function is the difference between the revenue and the cost functions.

P(x) = R(x) - C(x)

P(x) = -2x^2 + 478x - (4x + 18424)

P(x) = -2x^2 + 474x - 18424

The smallest break-even point is the smallest value of x at which profit is zero. Zero profit means there is no gain and no loss.

P(x) = -2x^2 + 474x - 18424 = 0

x^2 - 237x + 9212 = 0

9212 = 2^2 * 7^2 * 47

(x - 188)(x - 49) = 0

x - 188 = 0 or x - 49 = 0

x = 188 or x = 49

Answer: 49