Free Essay

Management Science

In: Business and Management

Submitted By leolui16
Words 432
Pages 2
Name: Lui Hei 15037621D

|1(i) |Definition of decision variables: | |
| |X1= No. of fresh hams produced | |
| |X2= No. of smoked hams produced on regular time |
| |X3= No. of smoked hams produced on overtime |
| |X4= No. of fresh pork bellies produced | |
| |X5= No. of smoked pork bellies produced on regular time |
| |X6= No. of smoked pork bellies produced on overtime |
| |X7= No. of fresh picnics hams produced | |
| |X8= No. of smoked picnics hams produced on regular time |
| |X9= No. of smoked picnics hams produced on overtime |
| | | | |
| |Algebraic linear programming formulation: | |
| | | | |
| |Maximize 8Xa+14Xb+11Xc+4Xd+12Xe+7Xf+4Xe+13Xg+9Xh |
| | | | |
| |Subject to |X1+X2+X3=480 | |
| | |X4+X5+X6=400 | |
| | |X7+X8+X9=230 | |
| | |X2+X5+X8 ≤ 420 | |
| | |X3+X6+X9 ≤ 250 | |
| | |X1+X2+X3+X4+X5+X6+X7+X8+X9≥0 | |

1(ii)
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2)

Let

X1 be the number of purchases of the canned goods in Sep

X2 be the number of purchases of the canned goods in Oct

X3 be the number of purchases of the canned goods in Nov

X4 be the number of purchases of the canned goods in Dec

X5 be the number of purchases of the canned goods in Jan

X6 be the number of purchases of the canned goods in Feb

X7 be the number of purchases of the canned goods in Mar

X8 be the number of purchases of the canned goods in Apr

X9 be the number of purchases of the canned goods in May

Objective function: 40X1+40X2+40X3+42X4+42X5+42X6+44X7+44X8+44X9+0.4Y1+0.4Y2+0.4Y3+0.4Y4+0.4Y5+0.4Y6+0.4Y7+0.4Y8

Subject to constraints:

X1-Y1=1000

X2+Y1-Y2=900

X3+Y2-Y3=850

X4+Y3-Y4=500

X5+Y4-Y5=600

X6+Y5-Y6=1000

X7+Y6-Y7=1000

X8+Y7-Y8=1000

X9+Y8-Y9=500

[pic][pic][pic]

3) Total payroll for the part time employee is $607.8647

20 part time shifts are needed

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[pic]

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-----------------------
Requirement constraint

Capacity constraint

Y1 be the number of inventory on hand in Sep

Y2 be the number of inventory on hand in Oct

Y3 be the number of inventory on hand in Nov

Y4 be the number of inventory on hand in Dec

Y5=be the number of inventory on hand in Jan

Y6 be the number of inventory on hand in Feb

Y7=be the number of inventory on hand in Mar

Y8 be the number of inventory on hand in Apr

Y9 be the number of inventory on hand in May

Demand constraint

Employment constraint…...

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