1. You have just taken a part-time job at Phil Bertz Nuthouse. Phil was pondering a new product, or maybe it was Bert? Well in any case, they are preparing a new product: a blend of mixed nuts. This blend will be sold in one-pound bags consisting of peanuts, almonds, cashews, and walnuts. Furthermore, the product mix must be at most 50% peanuts. Also, the blend must have more almonds than cashews. Finally, the blended mix must be at least 10% walnuts. Phil's goal is to mix the nuts in such a manner that all conditions discussed above are satisfied (the constraints), and the cost per bag is minimized. Peanuts cost $1.25 per pound, cashews cost $6 per pound, almonds cost $4 per pound, and walnuts cost $3 per pound. With your new knowledge of linear programming fresh in your mind, propose an optimum solution to your new boss!
Call the variables P, A, C, and W for the needed quantity (in pounds) of peanuts, almonds, cashews, and walnuts respectively.
Explain the LP process to Phil and Bert. What is LP? How is an LP problem defined?
Identify the decision variables of this problem.
Write out the objective function.
Determine two constraint equations for this LP problem, but do not solve! Hint: The number of constraint equations must equal the number of decision variables. Only two are required