Jungle Figures, Inc. produces two models of its stuffed giraffes, which it markets to high-end retail stores. The large giraffe requires 2 pounds of stuffing material and 6 minutes of machine time. The small giraffe requires 1 pound of stuffing material and 12 minutes of machine time since its tighter stitching pattern requires it to be stitched twice. There are 800 pounds of stuffing and 70 machine hours available each week. By adhering to a policy of not producing more than twice the number of large giraffes as small giraffes (this is a constraint), Jungle Figures has been able to sell all the giraffes it produces at $12 per large giraffe and $9 per small giraffe.

Formulate a linear programming model that maximizes Jungle Figures weekly profit from the manufacturing of the giraffes.

1. If Jungle Figures eliminates its policy of not producing more than twice the number of large giraffes as small giraffes, how will this affect the optimal solution?

2. Suppose 50 pounds of extra stuffing could be purchased for $200. Should Jungle do this? Would the optimal solution change?

3. Jungle is considering diverting 10 hours of machine time from the production of other products to produce giraffes. It figures it will lose $225 in gross profits from those products by this action. Should Jungle do this? Would the optimal solution change?

4. Suppose that demand is such that Jungle could effectively raise its prices to $15 on each giraffe (large or small). Would the optimal production schedule change?

5. Suppose demand for small giraffes waned, and Jungle cut its process so that its profit on small giraffes was reduced by 50% to $4.50. Would the optimal solution change?