NUMBER 5

LINEAR PROGRAMMING EXAMPLES - 1 --> what ifs? Example 1: The Candy Shop - a product mix problem 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 prepare for the season. A deluxe mix bag has 2/3 pounds of raisins and 1/3 pounds of peanuts and a standard mix bag has a half pound of raisins and a half pound of peanuts per bag. The shop has 100 pounds of raisins and 90 pounds of peanuts to work with. Peanuts cost $6.22 per pound and raisins cost $5.80 per pound. The deluxe mix will sell for $7.90 per bag and the standard mix will sell for $7.25 per bag. Based on demand in previous years the owner estimates that no more than 105 bags of deluxe mix will be needed but at least 40 bags of standard mix should be prepared. (a) If the candy store owner wishes to maximize profits, what should she do? Ans. make 105 deluxe and 60 standard mix bags, profit = $280.20 5. Solve Example 1 of the LP problems we formulated in class. (a) How many deluxe and standard mix bags should be made and what is the associated optimal profit? Consider each of the following independently in each case referring back to the original problem in (a) An extra 20 pounds of peanuts become available. Would you buy these extra peanuts and if so, how many deluxe and standard mix bags will be made and what is the associated optimal profit? Explain. 10 pounds of peanuts cannot be used because they were beyond their sale-by date. How does this affect your optimal solution? How many deluxe and standard mix bags will be made and what is the associated optimal profit? Explain. An extra 20 pounds of raisins become available. Would you buy these extra raisins and if so, how many deluxe and standard mix bags will be made and what is the associated optimal profit? Explain. 10 pounds of raisins cannot be used because they were beyond their sale-by date. How does this affect your optimal solution? How many deluxe and standard mix bags will be made and what is the associated optimal profit? Explain. Ans. (a) make 105 deluxe and 60 standard mix bags, profit = $280.20 (b) do not buy, we only use 65 pounds of the available peanuts, so why pay extra for more (c) no change, we have 45 pounds of peanuts left over unused (d) yes buy, make 105 deluxe and 100 standard mix bags, profit = $329.80 (e) make 105 deluxe and 40 standard mix bags, profit = $255.40