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 5 5
3 5 2

The shaper is available for 130 hours, and the grinder is available for 85 hours. No more than 350 units of component 3 can be sold, but up to 1050 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 $6, $7, and $8, respectively.

Required:
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 S4, should the company reduce the price?