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