Examples Of Linear Programming Problems And Solutions

Maximizing Total Annual Return

Part a

            The optimal solution for the solution is 5* 523.364486 + 8*1532.71028.

The value of the total annual return is 14878.50467.

 Part b

            The constraints Funds available and Risk Maximum are binding.

The objective’s for Funds available  

and Risk maximum  are the binding. Both the objectives are being used to the maximum value’s.

 Part c

The shadow price for “Funds available” is 0.1383. The shadow price for Risk maximum is 1.3084. Hence unit increase in the prices of the constraints would increase the “Funds available” by 0.1383 and “Risk Maximum” by 1.3084.

Part d

            The shadow price for Petroleum Inc. maximum is 0. Hence, any additional increase in the amount invested in Petroleum Inc. maximum would result in no increase in total annual return. Thus, investment in Petroleum Inc would not be beneficial.

Answer 2

Part a

The optimal solution for the solution is 2* 315.9565217 + 2.25 * 136.173913

The value of the total return based on the optimal solution is 938.3043478.

Part b

            The constraints Whole Tomatoes and Tomato Sauce are binding.

The objective’s for Whole Tomatoes is  

and for Tomato Sauce is  are the binding.

Both the objectives are being used to the maximum value’s.

Part c

The shadow price for “Whole Tomatoes” is 0.304348. The shadow price for “Tomato Sauce” is 0.119565. Hence unit increase in the value of the constraints would increase the “Whole Tomatoes” by 0.304348 and “Tomato Sauce” by 0.119565.

Part d

The right hand side ranges for Chopped Onions and jalapenos is 0 to 588.3043478. However, any increase in Chopped Onions and jalapenos would result in no increase in the optimal solution. Thus, there is no need to increase the amount of Chopped Onions and jalapenos.

 Answer 3

 Part a

From the solution it is seen that the Allowable increase for Units invested S is 5. Thus an increase in the Units Invested in S by units would not change the optimum solution for its present value of S = 4888.88 and M = 1666.666. 

Part b

From the solution it is seen that the Allowable increase for Units invested M is 1E+30. Thus an increase in the Units Invested in M by units would not change the optimum solution for its present value of S = 4888.88 and M = 1666.666. 

Part c

The allowable increase for “units purchased in stock fund” is 5 and for “units purchased in money market fund” is 1E+30. Thus increasing “units purchased in stock fund” from 10 to 12 and “units purchased in money market fund” from 4 to 6 would not change the optimum number of units purchased. Although, the total number of units purchased would increase.

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