Two products, A and B , require for their manufacturer spending a certain number

Question

Two products, A and B , require for their manufacturer spending a certain number of hours on stamping machine,a grinding machine, and a polishing machine. Product A requires 1 hour on the stamping machine, 2 hours on the grinding machine, and 2 hours on the polishing machine. Product B requires 2 hours on the stamping machine, 2 hours on the grinding machine,and 1 hour on the polishing machine. The stamping machine can operate 20 hours, the grinding machine 22 hours, and the polishing machine 15 hours each day. The profit on A and B is, respectively, $40 and $50 each.
Q1: In order to maximize company profits, p, from the two products to be manufactured, state the objective function in terms of a = the number of product A and b=the number of product B to be produced.

Q2: state the constraint for the grinding machine in terms of a= the number of product A and b= the number of product B to be produced.

Q3: state the constraint for the polishing machine in terms of a= the number of product A and b= the number of product B to be produced.
Two products, A and B , require for their manufacturer spending a certain number of hours on stamping machine,a grinding machine, and a polishing machine. Product A requires 1 hour on the stamping machine, 2 hours on the grinding machine, and 2 hours on the polishing machine. Product B requires 2 hours on the stamping machine, 2 hours on the grinding machine,and 1 hour on the polishing machine. The stamping machine can operate 20 hours, the grinding machine 22 hours, and the polishing machine 15 hours each day. The profit on A and B is, respectively, $40 and $50 each.
Q1: In order to maximize company profits, p, from the two products to be manufactured, state the objective function in terms of a = the number of product A and b=the number of product B to be produced.

Q2: state the constraint for the grinding machine in terms of a= the number of product A and b= the number of product B to be produced.

Q3: state the constraint for the polishing machine in terms of a= the number of product A and b= the number of product B to be produced.

Q1: In order to maximize company profits, p, from the two products to be manufactured, state the objective function in terms of a = the number of product A and b=the number of product B to be produced.

Q2: state the constraint for the grinding machine in terms of a= the number of product A and b= the number of product B to be produced.

Q3: state the constraint for the polishing machine in terms of a= the number of product A and b= the number of product B to be produced.

Explanation / Answer

Product Stamping Machine Grinding Machine Polishing Machine Product A 1 2 2 Product B 2 2 1 20 22 15 let no of Product A be "a" let no of Product B be "b" Based on the constraints given, the following linear equations can be derived 1) a+2b=20 2) 2a+2b =22 3) 2a+b=15 Objective function Z= 40a+50b

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