the times (in minutes) required on each machine are as follows: 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 to maximize profit. what are the optimal production quantities and the optimal profit? if more time could be made available on the grinder, how much would it be worth?