PLEASE HELP ME SOON

Question

A supply company manufactures copy machines. The unit cost C

 (the cost in dollars to make each copy machine) depends on the number of machines made. If x

 machines are made, then the unit cost is given by the function =Cx+−0.4x296x16,541

. What is the minimum unit cost?

Do not round your answer.

Answer 1

Unit cost is the Average Cost

Minimum Average Cost is where marginal cost = average cost

total cost = average cost times quantity. if x is the quantity produced, TC =AC times x

take the Average cost function (the per unit cost function), multiply it by x to get TC, the take the derivative which is the marginal cost. Set the marginal cost = average cost and solve for x

Best I can make of what you've written is

the average cost function might be: AC = C(x) = -0.4x^2 + 96x + 16,541 where 16,541 is the fixed cost and -04x^2 +96x is the average variable cost. But maybe you really gave us the total cost function. the numbers are run together in manner that doesn't makes sense

If that is AC, the TC = -0.4x^3 + 96x^2 + 16,541x take the derivative to solve for marginal cost: MC = TC' = -1.2x^2 + 192x + 16.541

set MC = AC

-0.4x^2 + 96x + 16541 = -1.2x^2 + 192x + 16541

0.8x^2 - 96x = 0

factor

.8x(x - 120) = 0

set the factors equal to zero to solve for x

x-120 = 0

x= 120 is the average cost minimizing output level

plug it back into the original C(x) function

C(120) = -0.4x^2 + 96x + 16,541 = -0.4(120)^2 + 96(120) + 16,541

= -0.4(14400) + 11520 + 16541

= -5760 + 28061

= $22,301 = minimum per unit cost

Just a stab in the dark for a solution, trying to decode the way you've written the problem. It does seem to come out to an integer solution, which is a small clue at least, maybe it's right.