For this homework, you will be formulating two Linear Programming Problems. DO N

Question

For this homework, you will be formulating two Linear Programming Problems. DO NOT SOLVE. Complete all work and submit solution on this worksheet PROBLEM #1 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. If the goal is to maximize profits, how many bags of each type should be prepared? What is the expected profit? SOLVE. Decision Variables: bjective Function: Constraints: PROBLEM #2 A retired couple supplement their income by making fruit pies, which they sell to a local grocery store. During the month of September, they produce apple and grape pies. The apple pies are sold for S1.50 to the grocer, and the grape pies are sold for $1.20. The couple is able to sell all of the pies they produce owing to their high quality. They use fresh ingredients. Flour and sugar are purchased once cach month. For the month of September, they have 1,200 cups of sugar and 2.100 cups of flour. Each apple pie requires 1 ½ cups of sugar and 3 cups of flour, and each grape pie requires 2 cups of sugar and 3 cups of flour. Determine the number of grape and the number of apple pies that will maximize revenues if the couple working together can make an apple pie in six minutes and a grape pie in three minutes. They plan to work no more than 60 hours. SOLVE

Explanation / Answer

1)

a) decision variables

x1 = number of deluxe mix to be prepared

x2 = number of standard mix of Peanut/raisin

b)

objective function

maximize Z = 2.9 *x1 + 2.55*x2 - 0.6*(1/3*x1 + 0.5*x2) - 1.5*(2/3*x1 + 1/2*x2)

c) constraints

x1 <= 110

x2 <= 110

1/3*x1 + 0.5*x2 <= 60

2/3*x1 + 1/2*x2 <= 90

Related Questions

Navigate

• Browse (All)
• Browse F
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.