PROBLEM #1 A small candy shop is preparing for the holiday season. The owner mus

Question

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?

FORMULATE THIS AS A LINEAR PROGRAM. DO NOT SOLVE.

Decision Variables:

Objective Function:

Constraints:

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?

Explanation / Answer

Decision variables:

Let

x represent bags of deluxe mix

y represent bags of standard mix.

The profit on the one-pound bag of deluxe mix is

$2.9 - $1.50(2/3) - $0.60(1/3) = $2.9 - $1 - $0.20 = $1.7

The profit on the one-pound bag of standard mix is

$2.55 - $1.50(1/2) - $0.60(1/2) = $2.55 - $0.75 - $0.30 = $1.5

Objective function is to maximize profits

Z = max 1.7x + 1.5y

Constraints:

x <= 110

y <= 110

(2/3)x + (1/2)y <= 90 [pounds of raisins available]

(1/3)x + (1/2)y <= 60 [pounds of peanuts]

x >= 0

y >= 0

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

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