Algebra

Linear Programming

Easy

A manufacturing company makes two types of television sets: one is black and white and the other is colour. The company has resources to make at most 300 sets a week. It takes Rs. 1800 to make a black and white set and Rs. 2700 to make a coloured set. The company can spend not more than Rs. 6,48,000 a week to make television sets. It makes a profit of Rs. 510 per black and white set and Rs. 675 per coloured set. Assuming x and y respectively are the number of black and white, and coloured sets made each week, answer the questions :

The maximum profit per week is :

Rs. 1,53,000

Rs. 1,72,800

Rs. 1,82,700

Rs. 1,62,000

✅ Correct Option: 2

Evaluate $z = 510x + 675y$ at each corner:

$z(0,0) = 0$

$z(300,0) = 153000$

$z(180,120) = 91800 + 81000 = 172800$

$z(0,240) = 162000$

Maximum profit is Rs. 1,72,800 at $(180, 120)$ .

Question 41

The objective function (z) to maximize the profit is:

Question 42

The constraints to the LPP are:

A. $3x + 2y \leq 720$

B. $2x + 3y \leq 720$

C. $x + y \leq 300$

D. $x \geq 0$ and $y \geq 0$

E. $x + y \geq 300$

Choose the correct answer from the options given below:

Question 43

The corner points of feasible region are:

A. (0, 240)

B. (0, 0)

C. (300, 0)

D. (120, 180)

E. (180, 120)

Choose the correct answer from the options given below:

Question 44

A feasible solution is :

The maximum profit per week is :

Solution

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