Assignment – Operation Economics

Operation Economics

1. i) Solve the following LP problem graphically:

 
 
Be sure to label your graph clearly – indicating (and labeling) the axes, the constraints, the feasible region, the highest attainable isoprofit line, the optimal solution etc. Also, be sure to give a complete written statement of the optimal solution, including the maximum attainable value of Z. In addition, state which constraint(s) is/are binding.
 

1. ii) Check your answer using LINDO. Be sure to attach the relevant LINDO output and to highlight the optimal solution.

 
 
FOR THE FORMULATION PROBLEMS BELOW, PLEASE BE SURE TO CLEARLY DEFINE ALL DECISION VARIABLES AND TO LABEL ALL CONSTRAINTS.
 
 

2. The Middletown Steel Company supplies castings to a variety of customers. It plans to devote the next week of production to just two of these customers: A Ltd. and B Ltd. Middletown uses a combination of pure steel and scrap metal to fulfill its orders and has 400 pounds of pure steel and 360 pounds of scrap metal in stock. The pure steel costs Middletown $6 per pound and the scrap metal costs Middletown $3 per pound. Pure steel requires 3 hours of processing time per pound to process into a casting, while scrap metal requires only 2 hours of processing time per pound to process into a casting. The total available processing time in the week is 2000 hours. The castings for A Ltd. each require 5 pounds of metal, with a quality restriction that limits the ratio of scrap metal to pure steel to a maximum of 5/7. A Ltd. has ordered 30 castings at a price of $50 each. The castings for B Ltd. each require 8 pounds of metal, with a quality control restriction that limits the ratio of scrap metal to pure steel to a maximum of 2/3. B Ltd. has ordered 40 castings at a price of $80 each.

 
Formulate an LP that can be used to maximize Middletown’s profit over the next week.
 
 

3. Farmer Giles grows soybeans and corn on his 45-acre farm. He can sell at most 140 bushels of soybeans and 120 bushels of corn. Each acre planted with soybeans yields 5 bushels and each acre planted with corn yields 4 bushels. Soybeans sell for $30 per bushel and corn sells for $50 per bushel. To harvest an acre of soybeans requires 6 hours of labour, whereas 10 hours of labour are required to harvest an acre of corn. Up to 450 hours of labour can be purchased at $12 per hour.

 
Formulate an LP that can be used to maximize Farmer Giles’ profits.
 
 

4. Consider Example 13 of Section 3.9 involving the manufacture of Brute and Chanelle perfumes. (Uploaded as a PDF, Book page 95-97)

 

1. i) Using LINDO, check that the optimal solution to the (correctly formulated) problem given in the textbook is correct. (Attach the relevant LINDO output and highlight the optimal solution.) Be sure to give a complete written statement of the optimal solution, including the maximum attainable profit. In addition, state which constraint(s) is/are binding.

 

1. ii) How does the optimal solution change if Constraint 1 is changed so that no more than 3000 pounds of raw material can be purchased annually? (Attach the relevant LINDO output and highlight the new optimal solution.) Be sure to give a complete written statement of the new optimal solution, including the maximum attainable profit. In addition, state which constraint(s) is/are binding.