Assume that the sale price of chairs is always sufficiently high that it is profitable to fulfill this 80-chair order. The firm needs to make 80 chairs to fulfill its order. Assume also that the firm is profit maximizing (& therefore cost minimizing).   What combinations of robot and worker hours must they use to minimize costs? Show your work. Use the equation that must be true for cost minimization

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)
14th Edition
ISBN:9781305506381
Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Chapter9: Applications Of Cost Theory
Section: Chapter Questions
Problem 2.1CE
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Assume that the sale price of chairs is always sufficiently high that it is profitable to fulfill this
80-chair order. The firm needs to make 80 chairs to fulfill its order. Assume also that the firm is
profit maximizing (& therefore cost minimizing).
 
What combinations of robot and worker hours must they use to minimize costs? Show
your work. Use the equation that must be true for cost minimization 
Suppose that there is a firm that produces chairs and the firm receives an order for 80 chairs. The
firm has two resources available to it. The first is a (human) worker, who must be paid $18 for
each hour they spend producing chairs. The second is a robot, that costs $15 of inputs (including
electricity and maintenance) for each hour it works. Chairs produced by either method are
identical and of equivalent quality.
Assume that the use of these two inputs is completely independent. This means that the number
of hours of robot-work does not affect the productivity of the worker, and vice versa.
The production of chairs based upon the numbers of hours of each of the inputs used is given
below. For example, 2 hours of robot time will produce 10 chairs. 7 hours of worker time will
produce 54 chairs.
Robot
Hours
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Robot
Production
0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
Robot
Hours
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Worker
Production
0
15
25
33
40
45
50
54
57
58
59
60
61
।
62
63
Transcribed Image Text:Suppose that there is a firm that produces chairs and the firm receives an order for 80 chairs. The firm has two resources available to it. The first is a (human) worker, who must be paid $18 for each hour they spend producing chairs. The second is a robot, that costs $15 of inputs (including electricity and maintenance) for each hour it works. Chairs produced by either method are identical and of equivalent quality. Assume that the use of these two inputs is completely independent. This means that the number of hours of robot-work does not affect the productivity of the worker, and vice versa. The production of chairs based upon the numbers of hours of each of the inputs used is given below. For example, 2 hours of robot time will produce 10 chairs. 7 hours of worker time will produce 54 chairs. Robot Hours 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Robot Production 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 Robot Hours 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Worker Production 0 15 25 33 40 45 50 54 57 58 59 60 61 । 62 63
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