Conan CPU manufactures two types of computers (desktops and laptops) using two o
ID: 379042 • Letter: C
Question
Conan CPU manufactures two types of computers (desktops and laptops) using two operations.
A desktop requires 2 hours of operation 1 and 1 hour of operation 2.
For laptops, one unit requires 1 hour of operation 1 and 3 hours of operation 2.
The revenues per unit of desktops and laptops are $30 and $20, respectively.
The total daily processing time available for each operation is 8 hours.
Sensitivity Report:
Variable Cells
Final
Reduced
Objective Allowable
Allowable
Cell Name
Value
Cost
Coefficient Increase
Decrease
$C$13 desktops
3.2
0
30 10
23.33333333
$D$13 laptops
1.6
0
20 70
5
Constraints
Final
Shadow
Constraint Allowable
Allowable
Cell Name
Value
Price
R.H. Side Increase
Decrease
$F$7 operation1
8
14
8 8
5.333333333
$F$8 operation2
8
2
8 16
4
The optimal objective function value for this problem is $128. Using the sensitivity report generated using Excel answer the following questions:
Suppose that the capacity of operation 1 is increased to 20 hours, how will this increase affect the optimum revenue? Explain and do not find new optimal value.
If the capacity of operation 1 is increased from 8 hours to 13 hours, how will this increase impact the optimum revenue? Explain and find the new optimal value.
A suggestion is made to increase the capacities of operations 1 and 2 at the additional cost of $10/hr for each operation. Is this advisable? Explain.
If Conan CPU can increase the capacity of both operations, which operation should receive priority? Explain.
Variable Cells
Final
Reduced
Objective Allowable
Allowable
Cell Name
Value
Cost
Coefficient Increase
Decrease
$C$13 desktops
3.2
0
30 10
23.33333333
$D$13 laptops
1.6
0
20 70
5
Constraints
Final
Shadow
Constraint Allowable
Allowable
Cell Name
Value
Price
R.H. Side Increase
Decrease
$F$7 operation1
8
14
8 8
5.333333333
$F$8 operation2
8
2
8 16
4
Explanation / Answer
1. Allowable increase for capacity of operation 1 is 8 only, So increase from 8 to 20 is more than the allowable increase, hence current basis do not remain optimal. However, optimum revenue will increase, but without solving the problem, we cannot determine the new optimal value from sensitivity report, shadow price is not valid for this change.
2. Increase from 8 to 13 is 5. It is within allowable range of increase. Therefore, shadow price is applicable. optimum revenue will increase by 14*5 = 70
New optimal value = 128+70 = 198
3. Shadow price of operation 1 is 14, which means every additional hour (upto the allowable increase) will yield incremental revenue of $ 14 . so capacity increase at cost of $ 10 per hour is economically viable.
However, it is not viable for operation 2, because its shadow price is 2, so it will result into loss of 2-10 = -8 for every additional hour.
4. operation 1 should receive priority because of high shadow price, it will yield comparatively more revenue ($ 14) per additional hour
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