Question

8. Samsung sells its four flagship products—cell phones, TVs, computing devices, and memory storage devices—through its exclusive showroom in a city. To support sales, it has hired 20 per-sons and trained them to service every product. Depending on the nature of the job, the cost of overhead expenses varies. The overhead cost of the cellphone section of the showroom per day is £70, for the TV section is £65, for the computing device section is £60, and for the memory storage section is £25. The store has allotted a budget of £1,000 for the showroom per day. A cell phone serviceman generates a revenue of £480 a day, a TV serviceman, £480, a computing devices serviceman, £450, and a memory storage section serviceman, £300. Each section needs at least two servicemen. The outlet wants to determine the number of servicemen to be assigned to each section that will maximize the revenue.

a. Formulate an integer programming model for this problem.

b. Solve this model by using the computer.

Answer 1

a) Let A, B, C and D be the number of servicemen alloted to cell phones, TVs, computing devices, and memory storage devices respectively. These are the decision variables.

The objective is to maximize the revenue. A cell phone serviceman generates a revenue of £480 a day, a TV serviceman, £480, a computing devices serviceman, £450, and a memory storage section serviceman, £300. Hence the objective function which is the total revenue, Z which needs to be maximized is as below

Z = 480A+480B+450C+300C

Now we come to the constraints. We have the below constraints.

As total number of service men cannot be more than 20, we have the below constraint

A+B+C+D 20

The overhead cost of the cellphone section of the showroom per day is £70, for the TV section is £65, for the computing device section is £60, and for the memory storage section is £25. As total budget is 1000, we have the below constraint

70A+65B+60C+25D 1000

As each section needs a minimum 2 service men, we have the below constraints

A 2

B 2

C 2

D 2

Also as the service men allocated to each of the section cannot be negative or fraction, we have the non-negativity constraint that that A, B, C and D should be positive integers

b) The problem is formulated in excel as below. The below 2 images show the formulation as well as the formulas used. The objective function to maximize is highlighted in green and the decision variables are highlighted in yellow.

Post these the solver parameters need to be entered as per the below image.

Once this is done, click on solve. The solver will solve the problem and show the message stating the same. Click on ok. The excel will now have the final solution as per below image.

Hence the final solution is as follows.

2 service men to cell phones section, 5 service men to TVs section, 6 service men to computing devices section and 7 service men to memory storage devices section. The maximum revenue possible is 8160.