Asked by Isaiah Tijero on Jul 21, 2024
Verified
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
Stamping Press
A machine used in manufacturing to shape or cut materials by deforming them with a die and high pressure.
Production Costs
Represents the total expenses incurred in the manufacturing of a product, including materials, labor, and overhead.
Chrysler Belvedere
A line of American automobiles produced by Chrysler from the 1950s to the 1970s, known for its stylish design and spacious interiors.
- Apply strategies aimed at reducing costs across different business decision-making scenarios.
Verified Answer
ZH
Zachary HarrillJul 28, 2024
Final Answer :
B
Explanation :
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 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.
Learning Objectives
- Apply strategies aimed at reducing costs across different business decision-making scenarios.