PROBLEMS 85 7 The Crumb and Custard Bakery makes coffee cakes and Danish pastries in t e pans. The main ingredients are flour and sugar. There are 25 pounds of flour and 16 wunds of available, and the demand for coffee cakes is 5. Five pounds of flour and 2 pounds of year are required to make a pan of coffee cakes, and 5 pounds of flour and 4 pounds of sugar we required to make a pan of Danish Apan of coffee cakes has a profit of $1. and a pan of Danish has a profit of 55. Determine the number of pans of cakes and Danich to produce cach day so that profit will be maximized a Formulate a linear programming model for this problem Solve this model hy in aphical analysis 8. In Problem 7 lw much flour and sugar will be left unused if the optimal numbers of cakes and Danish are baked? 9. Solve the following linear programming model graphically: maximize Z = 3x + 603 subject to 3x + 2x2 = 18 10 a drut from two ingredients. Each ingredient contains the Onem of ingredient contributes 3 units, an U n it of antibiotic 1: the drug requires 6 units. At least 4 uni d rend heredients contribute 1 unit each per gram. At least 12 un n e equired tem of ingredient i contributes 2 units, and a gram of ingredien Cun u nits. The cost raam of ingredient is $80, and the cost for a gram of ingredi 2 is $50. The company wants to formulate a linear programming model to determine the num of grams of each ingredient that must go into the drug to meet the antibiotic requirements at minimum cost. a Formulate a linear programming model for this problem, b. Solve this model by using graphical analysis. 11. A jewelry store makes necklaces and bracelets from gold and platinum. The store has 18 of gold and 20 ounces of platinum. Each necklace requires 3 ounces of gold and 2 oun platinum, whereas each bracelet requires 2 ounces of gold and 4 ounces of platinum. The de for bracelets is no more than four. A necklace cams $300 in profit and a bracelet. S100. Th wants to determine the number of necklaces and bracelets to make to maximize profit. a. Formulate a linear programming model for this problem. b. Solve this model by using graphical analysis. 12. In Problem 11. explain the effect on the optimal solution of increasing the profit on a from $400 to $600. What will be the effect of changing the platinum requirement for a from 2 ounces to 3 ounces? 13. In Problem 11: a. The maximum demand for bracelets is 4. If the store produces the optimal number of and necklaces, will the maximum demand for bracelets be met? If not, by how mu be missed? b. What profit for a necklace would result in no bracelets being produced, and what the optimal solution for this profit? 14. A clothier makes coats and slacks. The two resources required are wool cloth and clothier has 150 square yards of wool and 200 hours of labor available. Each coat requi yards of wool and 10 hours of labor, whereas each pair of slacks requires 5 square ya PROBLEMS 85 7 The Crumb and Custard Bakery makes coffee cakes and Danish pastries in t e pans. The main ingredients are flour and sugar. There are 25 pounds of flour and 16 wunds of available, and the demand for coffee cakes is 5. Five pounds of flour and 2 pounds of year are required to make a pan of coffee cakes, and 5 pounds of flour and 4 pounds of sugar we required to make a pan of Danish Apan of coffee cakes has a profit of $1. and a pan of Danish has a profit of 55. Determine the number of pans of cakes and Danich to produce cach day so that profit will be maximized a Formulate a linear programming model for this problem Solve this model hy in aphical analysis 8. In Problem 7 lw much flour and sugar will be left unused if the optimal numbers of cakes and Danish are baked? 9. Solve the following linear programming model graphically: maximize Z = 3x + 603 subject to 3x + 2x2 = 18 10 a drut from two ingredients. Each ingredient contains the Onem of ingredient contributes 3 units, an U n it of antibiotic 1: the drug requires 6 units. At least 4 uni d rend heredients contribute 1 unit each per gram. At least 12 un n e equired tem of ingredient i contributes 2 units, and a gram of ingredien Cun u nits. The cost raam of ingredient is $80, and the cost for a gram of ingredi 2 is $50. The company wants to formulate a linear programming model to determine the num of grams of each ingredient that must go into the drug to meet the antibiotic requirements at minimum cost. a Formulate a linear programming model for this problem, b. Solve this model by using graphical analysis. 11. A jewelry store makes necklaces and bracelets from gold and platinum. The store has 18 of gold and 20 ounces of platinum. Each necklace requires 3 ounces of gold and 2 oun platinum, whereas each bracelet requires 2 ounces of gold and 4 ounces of platinum. The de for bracelets is no more than four. A necklace cams $300 in profit and a bracelet. S100. Th wants to determine the number of necklaces and bracelets to make to maximize profit. a. Formulate a linear programming model for this problem. b. Solve this model by using graphical analysis. 12. In Problem 11. explain the effect on the optimal solution of increasing the profit on a from $400 to $600. What will be the effect of changing the platinum requirement for a from 2 ounces to 3 ounces? 13. In Problem 11: a. The maximum demand for bracelets is 4. If the store produces the optimal number of and necklaces, will the maximum demand for bracelets be met? If not, by how mu be missed? b. What profit for a necklace would result in no bracelets being produced, and what the optimal solution for this profit? 14. A clothier makes coats and slacks. The two resources required are wool cloth and clothier has 150 square yards of wool and 200 hours of labor available. Each coat requi yards of wool and 10 hours of labor, whereas each pair of slacks requires 5 square ya