3.4k views
5 votes
3. A company manufactures two types of products: A and B. Three resources R1, R2, and R3 are required to make these products. a. Each unit of product A requires 8 units of R1 and 4 units of R2. b. Each unit of product B requires 2 units of R1, 5 units of R2, and 3 units of R3. The availabilities of resources R1, R2, and R3 are 500, 400, and 180, respectively. The manufacturer also makes a profit of $20 and $50 for products A and B, respectively. Formulate a linear programming problem whose solution will tell the manufacturer how to maximize the total profit. • What are the decision variables? • What is the objective? • What is the objective function? • What are the constraints?

User Tahir Raza
by
8.8k points

1 Answer

1 vote

Answer:

(i)The units of production of Product A and B (x and y) are the decision variables

(ii)Objective is to maximize profit

(iii)Objective function, Max P=20x+50y

(iv)The Contraints are:

8x+2y
\leq500....(i)

2x+5y
\leq400.......(ii)

3y
\leq180

x>0, y>0

Step-by-step explanation:

Let the number of Product A=x

Let the number of Product B=y

Each unit of product A requires 8 units of R1 and 4 units of R2.

Each unit of product B requires 2 units of R1, 5 units of R2, and 3 units of R3

The availabilities of resources R1, R2, and R3 are 500, 400, and 180

Since R1
\leq500,

Product A requires 8 units of R1 per production unit

Product B requires 2 units of R1 per production unit

Total Unit of R1 possible is given by the inequality: 8x+2y
\leq500....(i)

Since R2
\leq400,

Product A requires 2 units of R2 per production unit

Product B requires 5 units of R2 per production unit

Total Unit of R2 possible is given by the inequality: 2x+5y
\leq400....(ii)

Since R3
\leq180,

Product B requires 3 units of R2 per production unit

Total Unit of R2 possible is given by the inequality: 3y
\leq180....(iii)

Since the manufacturer also makes a profit of $20 and $50 for products A and B, our objective is to maximize profit

Therefore: Objective function, Max P=20x+50y ......(iv)

User GRS
by
8.4k points

Related questions

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories