A garden supplies store prepares various grades of pine bark for mulch: nuggets (times 1), mini-nuggets C times 2), and chips (times 3). The process requires pine bark, machine time, labor time, and storage space. The following LP model has been developed Maximize 9 times 1 9 times 2 6 times 3 (profit) Subject to Bark 5 times 1 6 times 2 3 times 3 S 600 kg Machine 2 times 1 4 times 2 5 times 3 S 660 minutes Labor 2 times 1 4 times 2 3 times 3 S 480 hours Storage 1 times 1 1 times 2 1 times 3 S 150 bags times 1, times 2, times 3 0
a. Which decision variables are basic?
b. What is the marginal value (shadow price of a kilogram of pine bark? Over what range is this price value appropriate?
c. What is the maximum price the store should pay for additional pine bark?
d. What is the marginal value of labor? Over what range is this value in effect?
e. The manager obtained additional machine time through better scheduling How much additional machine time can be effectively used for this operation? Why?