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 :

A feasible solution is :

(120, 180)

(180, 120)

(0, 300)

(360, 0)

✅ Correct Option: 2

Check each point against $x+y \leq 300$ and $2x+3y \leq 720$ :

$(120,180)$ : $300 \leq 300$ ok; $240+540=780 > 720$ - fails.

$(180,120)$ : $300 \leq 300$ ok; $360+360=720 \leq 720$ ok - feasible.

$(0,300)$ : $300 \leq 300$ ok; $0+900=900 > 720$ - fails.

$(360,0)$ : $360 > 300$ - fails.

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 45

The maximum profit per week is :

A feasible solution is :

Solution

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