Operations Research Answers

Embassy Motorcycles (EM) manufactures two lightweight motorcycles designed for easy handling and safety. The EZ-Rider model has a new engine and a low profile that make it easy to balance. The Lady-Sport model is slightly larger, uses a more traditional engine, and is specifically designed to appeal to women riders. Embassy produces the engines for both models at its Des Moines, Iowa, plant. Each EZ-Rider engine requires 6 hours of manufacturing time, and each Lady-Sport engine requires 3 hours of manufacturing time. The Des Moines plant has 2000 hours of engine manufacturing time available for the next production period. Embassy’s motorcycle frame supplier can supply as many EZ-Rider frames as needed. However, the Lady-Sport frame is more complex and the supplier can only provide up to 280 Lady-Sport frames for the next production period.

Sony entertainment Television is planning to drop Shark Tank India show for four Friday evening programs at the end of the season. NP Singh, the CEO, asked to develop a list of six potential replacement programs. Estimates of the advertising revenue (Rs) that can be expected for each of the new programs in the four vacated time slots are as follows. Mr. Singh asked you to find the assignment of programs to time slots that will maximize total advertising revenue. 

Solve the following game

Player A

player B

Row (4)*Column(5)

R1-10,81,32,43,93

R2-59,63,39,69,73

R3-71,20,05,27,84

R4-34,14,44,44,69

4. A firm uses three machines in the manufacture of three products. Each unit of product requires 3 hours on machine I, two hours on machine II, and one hour on machine I While each unit of product B requires four hours on machine I, one hour on machine and three hours on machine III. While each unit of product C requires two hours on ea of the three machines. The contribution margin of the three products is birr 30, birr and birr 35 per unit respectively. The machine hours available on the three machines a 90, 54, and 93 respectively.

a. Formulate the above problem as a linear programing model

b. Obtain optimal solution to the problem by using the simplex method. Which of the three products shall not by produced by the firm? Why?

c. Calculate the unused capacity if any

d. What are the shadow prices of the machine hours?

Karamoja University has decided to build four buildings to house four departments. They have called for tenders from approved contractors for constructing the buildings. The scrutiny committee quotations for accounts felt that quotations of contractors A, B, C and D are reasonable and they decided to reject the remaining ones. The following table gives quotations in million shilling units of constructing the four buildings by the four respective contractors. Buildings Contractors || II IV A 10 24 30 15 В 16 22 28 12 12 20 32 10 26 34 16 (a) What decision the committee should make so that the amount to be spent by the University on construction is the minimum? (8 marks) (b) Suppose the scrutiny committee later on considers including contractor E in the selection of contractors. Determine the new schedule if contractor E quotes 12, 16, 22 and 15 units for the four buildings respectively.