A manufacturer of brand A jeans has daily production costs of Upper C equals 0.3 x squared minus 120 x plus 12 comma 585 , where C is the total cost (in dollars) and x is the number of jeans produced. How many jeans should be produced each day in order to minimize costs? What is the minimum daily cost?

a. 200 jeans should be produced each day in order to minimize costs.

b. The minimum daily cost is $108,585

a. 200 jeans should be produced each day in order to minimize costs.

b. The minimum daily cost is $108,585

Explanation:

a. How many jeans should be produced each day in order to minimize costs?

Given C = 0.3x^2 - 120x + 120,585 ... (1)

Cost is minimized when MC = C' = 0

To obtain MC, equation (1) is differentiate with respect to x as follows:

dC/dx = MC = C' = 0.6x - 120 = 0 ... (2)

From equation (2), we can now solve for x follows:

0.6x - 120 = 0

0.6x = 120

x = 120 : 0.6

x = 200

Therefore, 200 jeans should be produced each day in order to minimize costs.

b. What is the minimum daily cost?

Substitute 200 for x in equation (1) to have:

C = 0.3 (200^2) - 120 (200) + 120,585

= 12,000 - 24,000 + 120,585

C = $108,585

Therefore, the minimum daily cost is $108,585.