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scoundrel [369]
3 years ago
14

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?
Business
2 answers:
makvit [3.9K]3 years ago
8 0

Answer:

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.

Andrei [34K]3 years ago
7 0

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

b. The minimum daily​ cost is $108,585

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