The management scientist was planning to leave his actions up to the wisdom of his model, but before he could press "Solve" on his Excel spreadsheet, his wife weighed in on the project

Question

This was only reasonable, as it was her house before they tied the knot. It has been her dream to move back into this cottage once the management scientist goes to his great reward. She insists that the back door and garage door components of this project happen. If the variables have been chosen as in the table, construct an objective function and constraints that meet the management scientist's bride's requests.

x1 = contractor works on wood floors x2 = landlord works on wood floors
x3 = contractor works on kitchen tile x4 = contractor works on kitchen tile
x5 = contractor works on back door x6 = contractor works on back door
x7 = contractor works on garage door x8 = contractor works on garage door

Answer 1

Answer: Max Z = 100x1 + 100x2 + 80x3 + 80x4 + 15x5 + 15x6 + 20x7 + 20x8
Subject to:
x1 + x2 ≤ 1
x3 + x4 ≤ 1
x5 + x6 = 1
x7 + x8 = 1
2700x1 + 400x2 + 2500x3 + 1000x4 + 600x5 + 250x6 + 350x7 + 400x8 ≤ 3000
1x1 + 2x2 + 1.5x3 + 3x4 + 0.5x5 + 1x6 + 0.25x7 + 0.5x8 ≤ 4
x1, x2, x3, x4, x5, x6 , x7, x8 are 0,1