Linear Programming Question 40
Question: A shopkeeper wants to purchase two articles A and B of cost price Rs. 4 and 3 respectively. He thought that he may earn 30 paise by selling article A and 10 paise by selling article B. He has not to purchase total article worth more than Rs. 24. If he purchases the number of articles of A and B, x and y respectively, then linear constraints are
Options:
A) $ x\ge 0,\ y\ge 0,\ 4x+3y\le 24 $
B) $ x\ge 0,\ y\ge 0,\ 30x+10y\le 24 $
C) $ x\ge 0,\ y\ge 0,\ 4x+3y\ge 24 $
D) $ x\ge 0,\ y\ge 0,\ 30x+40y\ge 24 $
Show Answer
Answer:
Correct Answer: A
Solution:
Obviously $ x,y\ge 0 $ and $ 4x+3y\le 24 $ .
The cost price of article A is 4 and the shopkeeper wants to earn a profit of 30 paise by selling it.
Therefore, the selling price of article A is 4 + 0.30 = 4.30.
Similarly, the cost price of article B is 3 and the shopkeeper wants to earn a profit of 10 paise by selling it.
Therefore, the selling price of article B is 3 + 0.10 = 3.10.
The total cost of purchasing x articles of A and y articles of B is given by the equation: 4x + 3y ≤ 24
The total profit earned by selling x articles of A and y articles of B is given by the equation:
0.30x + 0.10y ≤ ?
The shopkeeper wants to maximize his profit, so we need to find the maximum value of
0.30x + 0.10y.
The linear constraints for this problem are:
4x + 3y ≤ 24
0.30x + 0.10y ≤ ?
The value of ? depends on the maximum profit the shopkeeper wants to earn.
BETA
