Question
Q: Develop a linear programming model for the given problem? RCT is a Remote control car toys manufacture produces four types of toys wheels, steel
Q: Develop a linear programming model for the given problem?
RCT is a Remote control car toys manufacture produces four types of toys wheels, steel wheels, aluminum wheels, and two are mixtures of aluminum and chrome wheels. Each wheel of all-Steel is made of 100% steel material, each wheel of all aluminum is made of 100% Aluminum material, each of type 3 wheel is made of 60% aluminum and 40% chrome. In addition, each of type 4 wheel is made of 30% aluminum and 70% chrome.
The following table illustrates the availability (per monthly production planning period) of the three materials used in the production process.
Material | kg of Material Available per Month |
Steel | 16,000 |
Aluminum | 60,000 |
Chrome | 33,000 |
Number of kilo grams required to make one wheel of all-Steel is 0.25 kg, Number of kilo grams required to make one wheel of all- Aluminum is 0.16 kg, Number of kilo grams required to make one wheel of type 3 is 0.20 kg , Number of kilo grams required to make one wheel of type 4 is 0.20 kg.
The manufacture has fixed contracts with several store to supply wheels. The contracts require that RCT manufacture supply a minimum quantity of each wheel, but allow for a larger demand if RCT manufacture chooses to meet that demand. The table below summarizes the contract demands for each of the four types of wheels.
Wheels Type | Minimum Monthly Demand | Maximum Monthly Demand |
Type #1 Steel | 60,000 | 140,000 |
Type #2 Aluminum | 200,000 | 280,000 |
Type #3 Aluminum Chrome | 19,000 | 320,000 |
Type #4 Aluminum Chrome | 120,000 | 170,000 |
RCT Manufacture goal is to maximize its monthly profit for product mix. The table below summarizes the profit price per wheel.
Varity of Wheel | All Steel | All Aluminum | Aluminum -Chrome Type 1 | Aluminum -Chrome Type 2 |
Profit $ | 815 | 614 | 712 | 800 |
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