Vollmer Manufacturing makes three components for sale to refrigeration companies. The components are processed on two machines: a shaper and a grinder. The times (in minutes) required on each machine are as follows:
Machine Component Shaper Grinder
1 6 4
2 4 5
3 4 2
The shaper is available for 120 hours, and the grinder is available for 110 hours. No more than 200 units of component 3 can be sold, but up to 1000 units of each of the other components can be sold. In fact, the company already has orders for 600 units of component 1 that must be satisfied. The profit contributions for components 1, 2, and 3 are $8, $6, and $9, respectively.
Formulate and solve for the recommended production quantities. If the constant is "1" it must be entered in the box.
Let:
C1 = units of component 1 manufactured
C2 = units of component 2 manufactured
C3 = units of component 3 manufactured
Maximize:
C1 + C2 + C3
Subject to:
6C1 + C2 + C3 ≤ 120 (Constraint 1)
C1 + C2 + 2C3 ≤ 110 (Constraint 2)
C3 ≤ 200 (Constraint 3)
C1 ≤ 1000 (Constraint 4)
C2 ≤ 1000 (Constraint 5)
C1 ≥ 600 (Constraint 6)
C1, C2, C3 ≥ 0
The optimal solution is:
C1 =
C2 =
C3 =
Profit = $