Question

GGV Corp. is considering the expansion of its networking and communication equipment
production. Four projects are being considered. Projects A and B are mutually exclusive, and
Projects C and D are mutually exclusive. Project C cannot be selected unless Project A or B has
been selected. Project D is an optional add-on of Project A. The company's board of directors
has approved $2 million for this expansion. In addition, because of limited personnel, only
27,000 labor hours can be committed to the expansion. Formulate the resource allocation
problem as a linear programming model. Use a MARR of 7.2% per year

	Progect A	Project B	Project C	Project D
Initial costs, $	410,000	560,000	595,000	635,000
Net annual revenue, $	54,000	69,000	72,500	77,500
Man-hours requirement, hours	11,000	12,500	12,950	13,250
Life, years	2	2	2	2

Answer 1

Solution:-

Goal

Maximize Z where Z = 54,000 XA + 69,000 XB + 72,500 XC + 77,500 XD

where,

Let XA denote whether or not Project A is selected. XA = 1 for selection of A and XA = 0 for rejection.

Let XB denote whether or not Project B is selected. XB = 1 for selection of B and XB = 0 for rejection.

Let XC denote whether or not Project C is selected. XC = 1 for selection of C and XC = 0 for rejection.

Let XD denote whether or not Project D is selected. XD = 1 for selection of D and XD = 0 for rejection.

Subject To :

Total Cost must be less than 2,000,000

410,000 XA + 560,000 XB + 595,000 XC + 635,000 XD <= 2,000,000

Total Man Hours required must not exceed 27000 hours

11,000 XA + 12,500 XB + 12,950 XC + 13,250 XD <= 27,000

MARR of 7.2% (Assuming Return = Net Annual Revenue/Project Cost)

54,000 XA + 69,000 XB + 72,500 XC + 77,500 XD >= 0.072 X ( 410,000 XA + 560,000 XB + 595,000 XC + 635,000 XD)

54,000 XA + 69,000 XB + 72,500 XC + 77,500 XD >= 29,520 XA + 40,320 XB + 42,840 XC + 45,720 XD

24,480 XA + 28,680 XB + 29,660 XC + 31,780 XD >=0

Project A & B are mutually exclusive

XA + XB <2

Project C & D are mutually exclusive

XC + XD <2

Project C needs either Project A or Project B

XA + XB - XC >=0

Project D is an optional add on of Project A

XA - XD >=0