Linear Algebra/Objective Function & Constraints

Question

Consider the problem:

“Wonder Widgets Co. manufactures three types of widgets: Standard Widget (SW), Gigantic Widget (GW), and Mini-Widget (MW) . Each widget must pass through four work centers. The SW requires 8 minutes in work center #1, 5 minutes in work center #2, 7 minutes in work center #3, and 4 minutes in work center #4. The GW requires 6 minutes in work center #1, 7 minutes in work center #2, 6 minutes in work center #3, and 4 minutes in work center #4. The MW requires 4 minutes in work center #1, 9 minutes in work center #2, 5 minutes in work center #3, and 8 minutes in work center #4. Each day, work center #1 has 7800 minutes available, work center #2 has 7500 minutes available, work center #3 has 7200 minutes available, and work center #4 has 6600 minutes available. The profits per widget are $7.50 for each SW sold, $9 for each GW, and $8.50 for each MW. If they can sell all the widgets they produce, how many of each should be manufactured each day in order to maximize profit?”

(a) Find the objective function

(b) Find the constraints

Answer 1

Nathan

Well if s, g, w are number produced per day

Profit = P = 7.5s + 9g + 8.5 w (objective functions)

Constraints

s,g,w >=0

8s + 6g + 4w <= 7800 (work center 1)

5s + 7g + 9m <= 7500 (work center 2)

7s + 6g + 5m <= 7200 (work center 3)

4s + 4 g + 8m <= 6600 (work center 4)

Mike