A small candy shop is preparing for the holiday season. The owner must decide ho
ID: 408468 • Letter: A
Question
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 1/3pound peanuts, and the standard mix has 1/2 pound raisins and 1/2 pound peanuts per bag I he 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 tor $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 die goal is to maximize, profits how many bags of each type should be prepared? What is the expected profit?Explanation / Answer
The owner should put out 110 bags of deluxe and 33 bags of standard mix.
Here are the constraints ...
Decision Variables are number of bags of deluxe and number of bags of standard
Let d = deluxe and s = standard
CONSTRAINTS
d 110
s 110
(2/3)d + (1/2)s 90
(1/3)d + (1/2)s 60
OBJECTIVE FUNCTION
Maximize Profit = 1.7d + 1.2s
Vertices of graph ...
(d, s)
(110,0)
(0,110)
(90,60)
(110,100/3)
(15,110)
Solution: (110,100/3)
Profit = 1.7d + 1.2s
= (1.7)(110) + (1.2)(33) = $226.60