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

Goal

Maximize Z where Z = 54,000 X_A + 69,000 X_B + 72,500 X_C + 77,500 X_D

where,

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

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

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

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

Subject To :

Total Cost must be less than 2,000,000

410,000 X_A + 560,000 X_B + 595,000 X_C + 635,000 X_D <= 2,000,000

Total Man Hours required must not exceed 27000 hours

11,000 X_A + 12,500 X_B + 12,950 X_C + 13,250 X_D <= 27,000

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

54,000 X_A + 69,000 X_B + 72,500 X_C + 77,500 X_D >= 0.072 X ( 410,000 X_A + 560,000 X_B + 595,000 X_C + 635,000 X_D)

54,000 X_A + 69,000 X_B + 72,500 X_C + 77,500 X_D >= 29,520 X_A + 40,320 X_B + 42,840 X_C + 45,720 X_D

24,480 X_A + 28,680 X_B + 29,660 X_C + 31,780 X_D >=0

Project A & B are mutually exclusive

X_A + X_B <2

Project C & D are mutually exclusive

X_C + X_D <2

Project C needs either Project A or Project B

X_A + X_B - X_C >=0

Project D is an optional add on of Project A

X_A- X_D>=0