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Linear programming questions using excel & analyze sensitivity

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Bradley Family

(a) Let X1 = # of acres of corn and X2 = # of acres of tobacco

Corn Tobacco Resources Available
300 520
Land 1 1 <= 410
Budget 105 210 <= 52500
Govt. Restriction 0 1 <= 100 Government Restriction

X1 X2
Decision Variables

Objective function

(b) How many acres of farm land will not be cultivated at the optimal solution?
Do the Bradleys use the entire 100 acre tobacco allotment?

('c) Should the Bradleys' lease extral land from their neighbor at $110 per acre?
What is the maximum price the Bradleys' should pay their neighbor? And how much land shoud they lease?

maximum price
# of acres of land

(d) For each dollar they borrow , how much additional profit will they make?
If they borrowed a additional $1000, would the number of acres of corn and tobacco they plant change?

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Solution Summary

The solution gives detailed steps on solving 4 linear programming questions using excel data analysis pack and then analyzing sensitivity report for each question.

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Linear Programming: Sensitivity Analysis and Interpretation of Solution

Vollmer Manufacturing makes three components for sale to refrigeration companies. The components are processed on two machines: a shaper and grinder. The times (in minutes) required on each machine are as follows:


Component Shaper Grinder
1 6 4
2 4 5
3 4 2

The shaper is available for 120 hours, and the grinder is available for 110 hours. No more than 200 units of components 3 can be sold, but up to 1000 units of each of the other components can be sold. In fact, the company already has orders for 600 units of component 1 that must be satisfied. The profit contributions for components 1, 2, and 3 are $ 8, $6, and $9, respectively.

a. Formulate and solve for the recommended productions quantities.
b. What are the objective coefficient ranges for the three components? Interpret these ranges for company management.
c. What are the right-hand-side ranges? Interpret these ranges for company management.
d. If more time could be made available on the grinder, how much would it be worth
e. If more units of components 3 can be sold by reducing the sales prices by $4, should the company reduce the price?

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