A small candy shop is preparing for the holiday season. The owner must decide how many bags of deluxe mix and how many bags of standard mix of Peanut/Raisin Delite to put up. The deluxe mix has 2/3 pound raisins and 1/3 pound peanuts, and the standard mix has 1/2 pound raisins and 1/2 pound peanuts per bag. The shop has 90 pounds of raisins and 60 pounds of peanuts to work with. Peanuts cost $.60 per pound and raisins cost $1.50 per pound. The deluxe mix will sell for $2.90 per pound, and the standard mix will sell for $2.55 per pound. The owner estimates that no more than 110 bags of one type can be sold.
1. If the goal is to maximize profits, how many bags of each type should be prepared? What is the expected profit?
2. If the selling price of the deluxe bags increased by $0.30 (to $3.20), would the optimal mix change? What would the total profit?
3. If the selling price of the standard bags decreased by $0.30 (to $2.25, would the optimal mix change? What would the total profit?
4. Would you be willing to purchase an additional 20 pounds of raisins for one dollar per pound (total cost of $20)? Why or why not? What would the new optimal solution be?