Question

1) After several years working as a corporate lawyer, a woman decides that she would prefer to start her own business. Her hobby is making pottery and she decides to turn her hobby into a business. After some experiments she decides to specialize in making cups and bowls. She sets her prices so that she will make a S2 profit on each cup and a profit of S1.50 on each bowl. You can assume that she sells every cup and every bowl that she makes. The woman has 40 hours per week to make the cups and bowls. It takes her 12 minutes to make a cup and 6 minutes to make a bowl. There are 60 minutes in an hour. Each week, the woman orders 125 kg of clay. (This is the raw material that pottery is made from.) Each cup uses 375g of clay. Each bowl uses 500g of clay. There are 1000g of clay in lkg of clay. Although she has many reasons for pursuing a new business, one of the reasons is to make money, and the woman would like the business to be as profitable as possible. a) (2 points) Use the letter C to represent the number of the cups and B to represent the number of bowls. Use the given information to write down the linear programming problem to maximize the weekly profit. b) (2 points) Solve the above programming problem by geometric solution method c) (3 points) By using the Simplex Algorithm find the maximum weekly profit.

Answer 1

(a)

From question, Number of cups = C and Number of bowls = B

Required to MAXIMIZE WEEKLY PROFITS, Z = 2*C + 1.5*B

Subject to Contraints:

• 12*C + 6*B = 2400 ................ Time constraint of 2400 minutes per week
• 375*C + 500*B = 125000....... Total clay available per week in grams

(b)

.

The maximum value of the objective function Z = 480, occurs at the extreme point (120,160).

Hence, the optimal solution to the given LP problem is : C =120, B =160 and max Z = 480.

(c)

Iteration-2 MinRatio 0.0833 - 400 0.5 50000 312.5 (312.5) 31.25 160 Z-400 0.1667 -0.5 T 0.1667

Hence, optimal solution is arrived with value of variables as :
C = 120, B = 160

Max weekly profits, Z=480