Question

JK Consulting is consider five different short term jobs opportunities. Each will require time in the next two months according to the table below.

Job	Time in first month	Time in second month	Revenue
V	4	6	16000
W	2	10	13000
X	8	15	18000
Y	12	8	5500
Z	5	3	16000

Revenue from each job is also shown. Develop a model whose solution would maximize revenue, meet the time budget of 30 hours in the first month and 25 hours in the second month, and not do both projects X and Y. TYPE IN MATHEMATICAL FORMULATION, NO SOLUTION NEEDED.

Answer 1

Let v,w,x,y and z be the binary decision variables. These variables can take the value of either 1 or 0. A value of 0 means the corresponding project is not selected while a value of 1 means the corresponding project is selected.

The objective is to maximize the revenue. Hence the objective function, Z which needs to be maximized is as below

Z = 16000v+13000w+18000x+5500y+16000z

We have 3 constraints in the problem. The first is that for first month we have 30 hours in total. Hence the constraint is as below

4v+2w+8x+12y+5z 30

The second constraint is that for second month we have 25 hours in total. Hence the constraint is as below

6v+10w+15x+8y+3z 25

The third constraint is that out of X and Y a maximum of 1 project can be done. Hence the constraint is as below

x+y 1

Hence the completed formulation is as below

Maximize Z = 16000v+13000w+18000x+5500y+16000z subject to constraints

4v+2w+8x+12y+5z 30

6v+10w+15x+8y+3z 25

x+y 1

(v, w, x, y, z) [0,1]