Question: 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                 Shape                  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.

a. Formulate and solve for the recommended production quantities.

b. What are the objective coefficient ranges for the three components? Interpret these ranges for company management.

c. What are the right-hand-side ranges? Interpret these ranges for company management.

d. If more time could be made available on the grinder, how much would it be worth?

e. If more units of component 3 can be sold by reducing the sales price by $4, should the company reduce the price?