What is the profit constraint?

Question

Billy Hill's Still
William J Hill runs a small batch artisnal bourbon distillery at a secluded location in the hills of Kentucky. He makes two products, known among his customers as Rotgut and White Lightning. The recipes for the two have been passed down in the Hill family for generations and are Rotgut: 1 bushel of corn, 3 pounds of sugar, 2 hours of cooking time. For the premium blend, White Lightning, he needs 2 bushels of corn, 2 pounds of sugar, and 3 hours of cooking time. Both recipes make enough to fill two jugs, which sell for $8 apiece for Rotgut and $12 apiece for White Lightning.

A quick inventory one crisp autumn morning reveals that William has on hand 40 bushels of corn, 70 pounds of sugar, and 50 jugs. He would like to brew up a few artisnal batches, but has recently received a tip that certain agencies have taken an interest in his talents and may be paying him a visit in three days, hence he plans to restrict any brewing activity to 72 hours at most, before he retreats to his home away from home, Lubbock.

William cleans his equipment, lights a fire, and ponders the objectives. Obviously the first priority is restricting himself to 72 hours of work — any more than that and he runs the risk of an extended holiday. His second priority to make enough to acquire materials for the next production run and fund his daughter's college tuition - he believes that $500 would make this production run worth his while. His third and fourth priorities are not to have too much perishable inventory, so he wants to make sure he doesn't have too many bushels of corn on hand (third priority) nor does he want too many pounds of sugar on hand (fourth priority).

Answer 1

Answer: 16R + 24W + d2+ + d2- = 500