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Jones Furniture Company produces beds and desks for college students. The production process requires carpentry and varnishing. Each bed requires 6 hours of carpentry and

Jones Furniture Company produces beds and desks for college students. The production process requires carpentry and varnishing. Each bed requires 6 hours of carpentry and 4 hour of varnishing. Each desk requires 4 hours of carpentry and 8 hours of varnishing. There are 36 hours of carpentry time and 40 hours of varnishing time available. Beds generate $30 of profit and desks generate $40 of profit. Demand for desks is limited, so at most 8 will be produced.

Let

X1 = Number of Beds to produce


X2 = Number of Desks to produce




The LP model for the problem is

MAX:

30 X1 + 40 X2

Subject to:

6 X1 + 4 X2£ 36 (carpentry)


4 X1 + 8 X 2£ 40 (varnishing)


X2£ 8 (demand for X2)


X1, X2³ 0




A

B

C

D

E

1


Jones Furniture



2






3


Beds

Desks



4

Number to make:




Total Profit:

5

Unit profit:

30

40



6






7

Constraints:



Used

Available

8

Carpentry

6

4


36

9

Varnishing

4

8


40

10

Desk demand


1


8







1.Refer to Scenario 3-1. What formula should be entered in cell E5 in the accompanying Excel spreadsheet to compute total profit?

2.Refer to Scenario 3-1. What formula should be entered in cell D8 in the accompanying Excel spreadsheet to compute the amount of carpentry used?

3. Refer to Scenario 3-1. Which cells should be changing cells in this problem?

4. Refer to Scenario 3-1. Which cells should be the constraint cells in this problem?

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