Question

Delicious Candy Company manufactures three types candy bars-Chompers, Smerks, and Delicious Chocolate. All three candies come in one-ounce size while Delicious Chocolate also comes in a one pound minibar bag. The basic ingredients used are chocolate, peanuts, and caramel. Delicious Chocolate is all chocolate, while Chompers consists of chocolate and caramel, and Smerks consists of chocolate, caramel and peanuts. Chompers’ recipe allows for the amount of caramel to be anywhere between 18% and 28% of the candy bar’s weight with chocolate making up the rest. Smerk’s recipe calls for an equal amount of caramel, and peanuts, with chocolate making up between 20% and 40% of the bar’s weight For each one-ounce bar, labor and packaging costs $0.012 while labor and packaging for the one-pound bag costs $0.039. The company has production facilities for making up to 20,000 one-ounce bars and up to 1000 one-pound bag daily. Delicious has contracts to produce at least 3000 one-ounce bars of each type of candy daily. Also the difference between the Chompers and the number of Smerks produced must be less than 10% of the total number of Chompers and Smekers made. The present prices for chocolate, caramel, and peanuts are $1.60, $0.95, and $1.40 per pound respectively. The company has contracts which will supply it with at least 1,000 pounds of chocolate, exactly350 pounds of caramel, and at most 500 pounds of peanuts daily. The company currently sells Chompers one-ounce bars for $ 0.14, Smerks one-ounce bars for $0.16, Delicious Chocolate one-ounce bars for $0.15, and Delicious Chocolate one-pound bags for $2.30. Formulate a linear program that would determine the optimal daily production schedule and ingredients required. (HINT: Variables must be established for each product type and the amount of each ingredient in each product.

Answer 1

Before making Linear Programing we have to fix the formulation of three candys. For that the best way is to keep the highest price ingradient to minimum % with in given range. Then the formula become

Ingradient	for 1 pound cost	for 1 ounce cost	Chomper	Smerk	Delicious Chocolate-1O	Delicious Chocolate-1P
Chocolate	1.6	0.1	72	20	100	100
Caramel	0.95	0.059375	28	40	0	0
Peanut	1.4	0.0875	0	40	0	0
Ingradient cost			0.088625	0.07875	0.1	1.6

Ingradients are in %

1ounce cost = 1pound cost/16

Now we can use Linear programming method to solve this

Quantiy of each variant in ounce can be denoted by

C- Chomper

S- Smerks

DO- Delicious Chocolate -1 ounce

DP- Delicious Chocolate -1 pound

Then Objective funtion should be

Max R = 0.14 xC + 0.16 x S + 0.15 x DO + DP/16 x 2.3

Constraints

0.72 C + 0.2 S+ 1.0 DO + 1.0DP <= 16000( 1000 pound =16000ounce)

0.28 C+ 0.40 S <= 5600

40S <=8000

C+S+DO <=20000

DP <=1000

C>=3000

S>=3000

DO>=3000

C-S <= 0.1 X (C+S)

This Problem can be solved by excel solver. For that we have to make tables like this

Variants	Chomper	Smerk	Delicious Chocolate-1O	Delicious Chocolate-1P
Qty
Rate	0.14	0.16	0.15	0.14375
Sale	0	0	0	0
Revenue	0
	Chomper	Smerk	Delicious Chocolate-1O	Delicious Chocolate-1P	Total	supply in pound		supply in ounce
Chocolate	72	20	100	100	0	1000	16	16000
Caramel	28	40	0	0	0	350	16	5600
Peanut	0	40	0	0	0	500	16	8000

Here Revenue = sum of sale values. This is the target value in excel solver

Then select Max,

Variable cells are qty cells

Then enter the constraints as said above.

Then the Solution is

No. of Chomper one ounce pack = 3000

No. of Smerk one ounce Pack = 11900

No. of Delicious Chocolate one ounce pack =5100

No. of Delicious Chocolate one pound pack =397