The Craine Company manufactures three products, which require three resources – labour, materials, and administration. The unit profits on these products are $10, $6, and $4 respectively. There are 100 hr of labour, 600 lb of material, and 300 hr of administrations available per day. In order to determine the optimal product mix, the following LP model is formulated and solved: Maximize Z =10 x 1 +6 x 2 +4 x 3 Subject to x1+x2+x3 ≤100 labour 10x1+4x2+5x3 ≤600 material 2x1+2x2+6x3 ≤300 administration x1+x2+x3 ≥0 Where x1,x2, and x3are the daily production levels of products 1, 2, and 3 respectively. A computer output of the solution given below: Optimal Solution: x1 = 33.33, x2 = 66.67, x3 = 0 Optimal Value: Maximum profit = $733.33 Shadow Prices: For row 1 = $3.33, for row 2 = 0.67, for row 3 = 0 Opportunity Costs For x1 = 0, for x2 = 0, for x3 = 2.67 Ranges on Objective Function Coefficients Row Lower Limit Present Value Upper Limit x1 6 10 15 x2 4 6 10 x3 -∞ 4 6.67 Ranges on Right-Hand-Side (RHS) Constraints Row Lower Limit Present Value Upper Limit 1 60 100 150 2 400 600 1000 3 200 300 ∞ Explain the sensitivity analysis from the problem above.
The Craine Company manufactures three products, which require three resources – labour, materials, and administration. The unit profits on these products are $10, $6, and $4 respectively. There are 100 hr of labour, 600 lb of material, and 300 hr of administrations available per day. In order to determine the optimal product mix, the following LP model is formulated and solved:
Maximize Z =10 x 1 +6 x 2 +4 x 3
Subject to x1+x2+x3 ≤100 labour
10x1+4x2+5x3 ≤600 material
2x1+2x2+6x3 ≤300 administration
x1+x2+x3 ≥0
Where x1,x2, and x3are the daily production levels of products 1, 2, and 3 respectively.
A computer output of the solution given below:
|
Optimal Solution: |
x1 = 33.33, x2 = 66.67, x3 = 0 |
|
Optimal Value: |
Maximum profit = $733.33 |
|
Shadow Prices: |
For row 1 = $3.33, for row 2 = 0.67, for row 3 = 0 |
|
|
For x1 = 0, for x2 = 0, for x3 = 2.67 |
Ranges on Objective Function Coefficients
|
Row |
Lower Limit |
Present Value |
Upper Limit |
|
x1 |
6 |
10 |
15 |
|
x2 |
4 |
6 |
10 |
|
x3 |
-∞ |
4 |
6.67 |
Ranges on Right-Hand-Side (RHS) Constraints
|
Row |
Lower Limit |
Present Value |
Upper Limit |
|
1 |
60 |
100 |
150 |
|
2 |
400 |
600 |
1000 |
|
3 |
200 |
300 |
∞ |
Explain the sensitivity analysis from the problem above.
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