The Chrysler Belvedere Truck Plant is attempting to minimize production costs.Over one month, 1,600 fenders are needed on the production line, which runs continuously.If it costs $200 to set up the stamping press to produce fenders and $1 per month to store produced fenders, how many times should the stamping press be run per month?
A)4 times
B)Twice
C)Once
D)3 times
E)5 times

Question

Quizplus · Accepted Answer

Let's assume that the stamping press runs "x" times in a month to produce 1,600 fenders.

The cost of setting up the stamping press = $200 per run
The cost of storing fenders per month = $1 per fender
Total cost = cost of setup + cost of storage = $200x + $1(1,600) = $200x + $1,600

To minimize the production cost, we need to find the optimal number of times the stamping press should be run. This can be done by finding the point where the cost is the lowest.

Let's take the derivative of the cost function:

d(cost)/dx = 200

Since the derivative is a constant, the cost function is a linear function. Therefore, the cost will be minimized when the stamping press is run as few times as possible.

To produce 1,600 fenders, the stamping press needs to be run:

1600/2 = 800 fenders per run
x = 1600/800 = 2 runs per month

Therefore, the stamping press should be run twice a month to minimize production costs.

The Chrysler Belvedere Truck Plant Is Attempting to Minimize Production