Problem 1: A factory makes tennis rackets and cricket bats. A tennis racket takes 1.5 hours of machine time and 3 hours of craftsman’s time in its making while a cricket bat takes 3 hour of machine time and 1 hour of craftsman’s time. In a day, the factory has the availability of not more than 42 hours of machine time and 24 hours of craftsman’s time. If the profit on a racket and on a bat is Php 20.00 and Php 10.00 respectively, find the maximum profit of the factory when it works at full capacity.
Solve for the following Linear Programming problems. Your solutions should include:
- Objective Function
- Constraints
- Graph complete with labels of points and lines, and shaded feasible region
- Corner point approach
- Optimal solution
- Maximum profit
Problem 1: A factory makes tennis rackets and cricket bats. A tennis racket takes 1.5 hours of machine time and 3 hours of craftsman’s time in its making while a cricket bat takes 3 hour of machine time and 1 hour of craftsman’s time. In a day, the factory has the availability of not more than 42 hours of machine time and 24 hours of craftsman’s time. If the profit on a racket and on a bat is Php 20.00 and Php 10.00 respectively, find the maximum profit of the factory when it works at full capacity.
Problem 2: A manufacturer produces nuts and bolts. It takes 1 hour of work on machine A and 3 hours on machine B to produce a package of nuts. It takes 3 hours on machine A and 1 hour on machine B to produce a package of bolts. He earns a profit of Php 35 per package on nuts and Php 14.00 per package on bolts. How many packages of each should be produced each day so as to maximize his profit, if he operates his machines for at the most 12 hours a day?
Write your answers on a sheet of graphing paper (or you may download and print your own graphing paper).
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