Question

 

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 Excel QM for windows or solver.

Answer 1

a.

Let,

xi = number of person attended to each section i where i = {cell phones=1, TVs=2, computing devices=3, and memory storage devices=4}

objective is to maximize revenue = max 480x1+480x2+450x3+300x4

subject to,

(Budget)           70x1+65x2+60x3+25x4<=   1000
Total no of service person   1x1+x2+x3+x4 <=   20
Min no of sales person       x1>=   2
               x2>=   2
               x3>=   2
               x4>=   2

xi >= 0, xi = integer

b.

Solving in solver we get,

Number of person to alotted to cell phones=2, TVs=5, computing devices=6, and memory storage devices=7}

MAximized revenue = 8160

Solver screenshot

Solver formula

Solver window