Question

The Chick’n -Pick’n fast-food restaurant chain is considering how to expand its operations. Three types of retail outlets are possible: a lunch counter operation designed for office buildings in downtown areas, an eat-in operation designed for shopping malls, and a stand-alone building with drive-through and sit-down facilities. The following table summarizes the number f jobs, start up costs, and annual returns associated with each type of operations

	Lunch Counter	Mall	Stand-Alone
Jobs	9	17	35
Costs	150,000	275,000	450,000
Returns	85,000	125,000	175,000

The company has $2,000,000 available to pay start up costs for new operations in the coming year. Additionally, there are five possible sites for lunch counter operations, seven possible mall locations, and three possible stand-alone locations. The company wants to plan its expansion in a way that maximizes annual returns and the number of jobs created.

1.     Formulate the MOLP for this problem.

2.     Implement the model in a spreadsheet.

3.     Determine the best possible value for each objective in the problem.

4.     Implement the model in a spreadsheet and solve it to determine the solution that minimizes the maximum percentage deviation from the optimal objective function values. What solution do you obtain?

5.     Suppose management considers maximizing returns three times as important as maximizing the number of jobs created. What solution does this suggest?

Answer 1

Answer 1: X1=number of lunch counter units built

X2=number of mall units built

X3=number of standalone units built

            Max (z)               85 X1 + 125 X2 + 175 X3     (Profit)

            Max (z)                         9 X1 +   17 X2 +   35 X3        (jobs created)

              Constraints        150 X1 +   275 X2 +   450 X3   2000

X1< 5

X2< 7

X3<3

Answer 2 (excel sheet formula maximize explanation)
	X1	X2	X3
	5	4.54545454545455	0
objective (Z)	85	125	175	=(C5*C4+D5*D4+E5*E4)+(C6*C4+D6*D4+E6*E4)
	9	17	25
CONSTRAINT	=G8*C4+H8*D4+I8*E4	<	2000
	=C4	<	5		150	275	450
	=D4	<	7
	=E4	<	3
	=C4	>	0
	=D4	>	0
	=E4	>	0