Big Bus Company produces buses.In order to produce the seats for the buses,special equipment must be set up.The setup cost per frame is $40.The cost of carrying seats in inventory is $5 per seat per year.The company produces 100,000 buses per year. What is the number of seats that should be produced per setup in order to minimize the total setup and carrying costs?
A)566 seats
B)894 seats
C)1,265 seats
D)2,828 seats

Question

Quizplus · Accepted Answer

Let x be the number of seats produced per setup.
The total setup cost can be expressed as $40*(100000/x). The total carrying cost can be expressed as $5*x/2 since the average inventory level is x/2.
Thus, the total setup and carrying cost can be expressed as 40*(100000/x) + 5*x/2.
To minimize this cost, we take the derivative with respect to x, set it equal to zero, and solve for x:
d/dx [40*(100000/x) + 5*x/2] = -4000000/x^2 + 5/2 = 0
x^2 = (4000000*2)/5 = 1600000
x = 1265.8
Since we cannot produce a fractional number of seats, we round up to the nearest whole number: x = 1265.
Therefore, the number of seats that should be produced per setup in order to minimize the total setup and carrying costs is 1265 seats.

Big Bus Company Produces Buses