Question

TASTY bakery bakes two types of cakes-A and B. Cake A requires 20grams of flour, 10...

TASTY bakery bakes two types of cakes-A and B. Cake A requires 20grams of flour, 10 grams of sugar, and 10 grams of butter. Cake B requires 15grams of flour, 20 grams of sugar, and 5 grams of butter.

   The bakery only has 200 grams flour, 150 grams sugar, and 120 grams butter. The price of each cake A is $5 and price of each cake B is $4. Under the above circumstances, find out how many cakes of each type TASTY should bake to maximize revenue.

Business   Operations-Management   
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Homework Answers

Answer #1

The objective function is

Max 5 X1+4X2

where X1 and X2 are the number of A and B type of cakes baked respectively

Subject to contraints

20X1+15X2<=200

10X1+20X2 <= 150

10X1+5X2 <= 120

and X1, X2 =>0

Sloving by graphical method, we get the points ( 10,0) ( 7,4) and ( 0, 7.5)

Putting in the objective function, we get

Value at (10,0) =5x10 +0 =50

Value at (7,4) = 7x5 + 4x4 =51

Value at ( 0, 7.5) = 0+4x7.5 =30

As the value of the objective function is highest at ( 7,4) producing 7 units of cake A and 4 units of B willyield best profit.

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