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.
