ECON 4004 A Fall 2017 Simon Power
PLEASE BE SURE TO READ THE DOCUMENT ENTITLED: “GENERAL ASSIGNMENT GUIDELINES” (available for download from cuLearn) BEFORE YOU BEGIN THIS ASSIGNMENT. SEE SECTION 4.9 AND APPENDIX A OF CHAPTER 4 FOR INSTRUCTIONS ON THE USE OF LINDO.
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.
ii) Check your answer using LINDO. Be sure to attach the relevant LINDO output and to highlight the optimal solution.
FOR THE FOLLOWING TWO FORMULATION PROBLEMS, BE SURE TO CLEARLY DEFINE ALL DECISION VARIABLES AND TO LABEL ALL CONSTRAINTS. YOU DO NOT NEED TO ACTUALLY SOLVE THESE TWO FORMULATION PROBLEMS.
2. Ottawa City Council is trying to decide how to allocate its promotional budget of $18,200 for this year’s To-Die-For Donut Festival. Advertising alternatives include television, radio, and newspaper. For television, the estimated audience per advertisement is 100,000 people and the average cost per advertisement is $2,000. For radio, the estimated audience per advertisement is 18,000 people and the average cost per advertisement is $300. While, for newspaper, the estimated audience per advertisement is 40,000 people and the average cost per advertisement is $600. To satisfy local sensibilities in the broader public relations industry, the city feels that that there should be limits on how many advertisements should be produced by each type of media. Specifically, it is felt that there should be no more than 10 television advertisements, no more than 20 radio advertisements, and no more than 10 newspaper advertisements. Finally, to satisfy the Ontario Advertising Standards Council requirements that advertising by public entities should be balanced, no more than 50% of the total number of advertisements should be on radio and at least 10% of the total number of advertisements should appear on television.
Formulate an LP that can be used to determine how the promotional budget should be allocated among the three types of advertising alternatives in order to maximize the total audience contact.
3. An automobile manufacturing company produces three lines of cars: Sub-Compact, Compact, and Mid-Sized, with fuel efficiency ratings of 32, 24, and 17 miles per gallon. It must produce at least 100,000 cars in the coming year and in order to satisfy federal environmental legislation the average fuel efficiency rating of cars produced must be at least 25 miles per gallon. Because of the high profit margin, the company would like to produce at least 25,000 Mid-Sized cars. The capacity of their engine plant for the smaller models limits production of Sub-Compacts and Compacts to a total of 90,000. The current MSRP prices of the three types of cars are $14,500, $19,000, and $23,000 for the Sub-Compact, Compact, and Mid-Sized, respectively. Most cars are expected to sell at these MSRP prices, but based on past experience the company expects that 10% of the Sub-Compacts and Compacts produced will have to be sold at a 15% discount and that 20% of the Mid-Sized cars will have to be sold at a 20% discount.
Formulate an LP for this problem that can be used to maximize the company’s sales revenue.
4. Consider Example 15 of Section 3.11 involving an optimal investment strategy for Finco Investment Corporation:
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 amount of cash on hand at time 3. In addition, state which constraint(s) is(are) binding.
ii) How does the optimal solution change if the maximum amount that can be invested in investment E is restricted to be $50,000, rather than $75,000? (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 amount of cash on hand at time 3. In addition, state which constraint(s) is(are) binding.
