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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+2y500....(i)
2x+5y400.......(ii)
3y180
x>0, y>0
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 500,
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+2y500....(i)
Since R2 400,
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+5y400....(ii)
Since R3 180,
Product B requires 3 units of R2 per production unit
Total Unit of R2 possible is given by the inequality: 3y180....(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)