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MAT540 Week 8 Homework
Chapter 4
14. Grafton Metalworks Company produces metal alloys from six different ores it mines. The company has an order from a customer to produce an alloy that contains four metals according to the following specifications: at least 21% of metal A, no more than 12% of metal B, no more than 7% of metal C and between 30% and 65% of metal D. The proportion of the four metals in each of the six ores and the level of impurities in each ore are provided in the following table:
Ore
Metal (%)
Impurities (%)
Cost/Ton

A
B
C
D

1
19
15
12
14
40
27
2
43
10
25
7
15
25
3
17
0
0
53
30
32
4
20
12
0
18
50
22
5
0
24
10
31
35
20
6
12
18
16
25
29
24 …show more content…
The times required by the various operators to perform the required operations on each machine are summarized as follows: Operator
Drill Press (min)
Lathe (min)
Grinder (min)
1
23
18
35
2
41
30
28
3
25
36
18

Joe Henderson wants to assign one operator to each machine so that the topal operating time for all three operators is minimized.
a. Formulate a linear programming model for this problem.
b. Solve the model by using the computer
c. Joe’s brother, Fred, has asked him to hire his wife, Kelly, who is a machine operator. Kelly can perform each of the three required machine operations in 20 minutes. Should Joe hire his sister-in-law? 43. The Cash and Carry Building Supply Company has received the following order for boards in three lengths:
Length
Order (quantity)
7 ft.
700
9 ft.
1,200
10 ft.
300

The company has 25-foot standard-length boards in stock. Therefore, the standard-length boards must be cut into the lengths necessary to meet order requirements. Naturally, the company wishes to minimize the number of standard-length boards used. a. Formulate a linear programming model for this problem.
b. Solve the model by using the computer
c. When a board is cut in a specific pattern, the amount of board left over is referred to as “trim-loss.” Reformulate the linear programming model for this problem, assuming