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

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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