a dealer wish to purchase a number of fanand sawing machines. he has only ₹ 5760 to invest and has space for 20 items. A fan costs him ₹360 and a sawing machine ₹ 240. his expectations is that he can sell a fan at profit of ₹ 20 and sawing machine at profit of ₹ 18. assuming that he call sell all the items that he can buy. how should he invest his money in order to maximize his money formulate it as a L. P. P and thenthen use the graphical method to solve
Answers
Answer:
Suppose the dealer buys x fans and y sewing machines. Since the dealer has space for at most 20 items. Therefore,
A fan costs Rs. 360 and a sewing machine costs Rs. 240. Therefore, total cost of x fans and y sewing machine is Rs. (360 x + 240y). But the dealer has only Rs.5760 to invest.
Therefore,
Since the dealer can sell all the items that he can buy and the profit on a fan is Rs.22 and on a sewing machine the profit is of Rs. 18. Therefore, total profit on selling x fans and y sewing is of Rs. (22 x + 18 y).
Let Z denote the total profit. Then, Z = 22x + 18y.
Clearly,
Thus, the mathematical formulation of the given problem is
Maximize Subject.
To solve this LPP graphically, we first convert the in equations into equations and draw the corresponding lines. The feasible region of the LPP is shaded in Figure. The corner points of the feasible region OA2 PB1 are (0, 0), A2 (16, 0), P(8, 12) and B1 (0, 20).
These points have been obtained by solving the corresponding intersecting lines, simultaneously.
The values of the objective function Z at corner – points of the feasible region are given in the following
Point (x, y)
Value of the objective function
Z = 22 x+ 18y
Clearly, Z is maximum at x = 8 and y = 12. The maximum value of Z is 392.
Hence, the dealer should purchase 8 fans and 12 sewing machines to obtain the maximum profit under given conditions.
