Question

A furniture dealer sells only tables and chairs. He has Rs. 12,000 to invest and a space to store 90 pieces. A table costs him Rs. 400 and a chair Rs. 100. He can sell a table at a profit of Rs. 75 and a chair at a profit of Rs. 25. Assume that he can sell all the items. The dealer wants to get maximum profit.

(i) By defining suitable variables, write the objective function.

(ii) Write the constraints.

(iii) Maximise the objective function graphically.

Answer 1

(i) Let x be the number of Tables and y be the number of Chairs. Then; Maximise; z = 75x + 25y

(ii) Furniture constraints x + y < 90

Investment constraint 400x + 100y < 12000

Therefore;Maximise; Z = 75x + 25y, x + y < 90, 4x + y < 120, x<0, y<0

(iii) In the figure the shaded region OABC is the feasible region. Here the region is bounded. The corner points are O(0, 0), A(30, 0) B(10, 80), C(0, 90)

Given; Z = 75x + 25y

Corner points	Value of Z
O	Z =75(0) +25(0) = 0
A	Z= 75(30)+ 25(0) = 2250
B	Z= 75(10)+ 25(80) = 2750
C	Z= 75(0)+ 25(90) = 2250

Since minimum value of Z occurs at B, the soluion is Z = 2750.