Mathematical optimization /operations research

Acids food processing plant which vanufactures hamburger bups and burger paties. Thex grind their own Pour for the hamburger buns, at a maximum rats of 200 kilograms per week. Each hamburger bun requires 0.1 kes of flour Thex cuently have a contact with Scowood, Inc. which specifies that a delivery of 800 kgs of meat product is delixcred every Mondax Each hamburger patty tequires 4 kgs of minced oca All the other ingredients in the hamburger pattics and hamburger buds are in plentiful supply Finally the labor force at Acous consists of 5 employees working full time (40 hours per week sach). Each hamburger patx tequires 3 minutes of labor, and each hamburger bun requires 2 minutes of labor Each hamburger patty yields a profit of $0.20, and each hamburger ban vields a profit of $0.10. Asms, would like to know how many hamburger potties and how many hamburger buus thex should produce each week so as to acbiexe the highest possible profil (a) Formulate a linear programming model for this problem. (b) Use the granical method to solve this model. The Metsan co. desiss to blend a new alox of 40 percent copper, 35 percent brass, and 25 peccent silver from sexexhavailable aloxs boxing the following properties 1 60 2 25 Alley 3 4 45 20 5 50 10 15 45 50 40 Percentage of copper Percentage of brass. Percentage of silver Cost (S/kg) 30 60 10 30 10 110 100 125 120 135 The obiective is to determine the proportions of these alors that should be blended to produce the new allax at a minimum cost. (a) oppuate a linear peramping model for this problem. (b) Solve this model by the simplex method