Creative Sports Designs (CSD) manufactures a standard-size tennis racket (X) and an oversize tennis racket (Y). The firm’s rackets are extremely light due to the use of a magnesium-graphite alloy that was invented by the firm’s founder. Each standard-size racket, X, uses 125 grams of the alloy and each oversize racket, Y, uses 400 grams; over the next 2-week production period only 80 kilograms of the alloy are available (there are 1000 grams in one kilogram). Each X uses 10 minutes of manufacturing time and each Y uses 12 minutes. The profit contributions are $10 for each X and $15 for each Y. 40 hours of manufacturing time are available each week. Management has specified that at least 20% of the total production must be X (the standard-size racket). CDS is required to produce a minimum of 50 oversize tennis racket. How many rackets of each type should CSD manufactured over the next 2 weeks to maximize the total profit contribution? Formulate a linear programming model for this problem and solve it using the graphical method. Your file should contain the following information: 1) A linear programming model where decision variables are clearly identified, 2) A graph showing all constraints with feasible region clearly identified 3) A table showing all extreme corners in the feasible region with optimal solution.
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
Creative Sports Designs (CSD) manufactures a standard-size tennis racket (X) and an oversize tennis racket (Y). The firm’s rackets are extremely light due to the use of a magnesium-graphite alloy that was invented by the firm’s founder. Each standard-size racket, X, uses 125 grams of the alloy and each oversize racket, Y, uses 400 grams; over the next 2-week production period only 80 kilograms of the alloy are available (there are 1000 grams in one kilogram). Each X uses 10 minutes of manufacturing time and each Y uses 12 minutes. The profit contributions are $10 for each X and $15 for each Y. 40 hours of manufacturing time are available each week. Management has specified that at least 20% of the total production must be X (the standard-size racket). CDS is required to produce a minimum of 50 oversize tennis racket. How many rackets of each type should CSD manufactured over the next 2 weeks to maximize the total profit contribution?
Formulate a linear programming model for this problem and solve it using the graphical method.
Your file should contain the following information:
1) A linear programming model where decision variables are clearly identified,
2) A graph showing all constraints with feasible region clearly identified
3) A table showing all extreme corners in the feasible region with optimal solution.
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