10) Natural Furniture Company manufactures three outdoor products, chairs, benches, and tables. Each product must pass through the following departments before it is shipped: sawing, sanding, assembly, and painting. The time requirements (in hours) are summarized in the tables below.
The production time available in each department each week and the minimum weekly production requirement to fulfill contracts are as follows:
Minimum |
|||
Capacity |
Production |
||
Department |
(In Hours) |
Product |
Level |
Sawing |
450 |
Chairs |
100 |
Sanding |
400 |
Benches |
50 |
Assembly |
625 |
Tables |
50 |
Painting |
550 |
Hours Required |
Unit |
||||
Product |
Sawing |
Sanding |
Assembly |
Painting |
Profit |
Chairs |
1.5 |
1.0 |
2.0 |
1.5 |
$15 |
Benches |
1.5 |
1.5 |
2.0 |
2.0 |
$10 |
Tables |
2.0 |
2.0 |
2.5 |
2.0 |
$20 |
The production manager has the responsibility of specifying production levels for each product for the coming week. Formulate as a linear programming problem to maximize profit. Explain your findings?
- Based on problem #10, how many constraints are in this problem?
A. 3
B. 4
C. 7
D. 10
- Based on problem #10, how many units of the Chair and Table would be produced based on this solution?
A) 113, 100
B) 50, 113
C) 100, 50
D) 100, 113
- Based on problem #10, how many units of the Chair and Bench would be produced based on this solution?
A) 113, 100
B) 50, 113
C) 100, 50
D) 100, 113
- Based on problem #10, what is the optimal solution based on objective function (rounded to nearest decimal place):
A) 4250
B) 4000
C) 3625
D) 3688
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