Each machine at a certain factory can produce 90 units per hour. The setup cost is 45 dollars for each machine and the operating cost is 19 dollars per hour (total, not 19 dollars per machine per hour). You would like to know how many machines should be used to produce 10000 units, with the goal of minimizing production costs. First, find a formula for the total cost in terms of the number of machines, n: TC = 45n+19(10000/(90n)) The minimum total cost is achieved when using machines for a total cost of dollars.

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Each machine at a certain factory can produce 90 units per hour. The setup
cost is 45 dollars for each machine and the operating cost is 19 dollars per hour
(total, not 19 dollars per machine per hour). You would like to know how many
machines should be used to produce 10000 units, with the goal of minimizing
production costs.
First, find a formula for the total cost in terms of the number of machines, n:
TC =
45n+19(10000/(90n))
The minimum total cost is achieved when using
machines for a total cost of
dollars.
Transcribed Image Text:Each machine at a certain factory can produce 90 units per hour. The setup cost is 45 dollars for each machine and the operating cost is 19 dollars per hour (total, not 19 dollars per machine per hour). You would like to know how many machines should be used to produce 10000 units, with the goal of minimizing production costs. First, find a formula for the total cost in terms of the number of machines, n: TC = 45n+19(10000/(90n)) The minimum total cost is achieved when using machines for a total cost of dollars.
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