Volmer Manufacturing

Volmer Manufacturing makes three components (labeled below as X, Y, Z) for sale to refrigeration companies. The components are processed on two machines: a shaper and a grinder. The time (in minutes) required for each component, on each machine are as follows:

	Machine
Component	Shaper	Grinder
X	6	4
Y	4	5
Z	4	2

The shaper is available for 120 hours, and the grinder is available for 110 hours. No more than 200 units of component Z 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 X that must be satisfied. The profit contributions for components X, Y and Z are $8, $6, and $9, respectively.

1. In the Volmer Manufacturing problem (where X, Y and Z stand for the quantity of components sold), how many minutes are used on the shaper if Volmer sells 600 units of X, 400 units of Y and 200 units of Z?

2. In the Volmer Manufacturing problem (where X, Y and Z stand for the quantity of components sold), what is the formula for constraint that "up to 1000 units of component X can be sold"?

3. In the Volmer Manufacturing problem (where X, Y and Z stand for the quantity of components sold), how much profit does the company make if Volmer sells 350 units of X, 350 units of Y and 200 units of Z?