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XYZ Manufacturing Company produces three types of expresso machines: Grade-A model, Grade-B model, and Grade C model. The Grade-A model is sold at a unit price of $750 per unit; Grade-B model is sold at $600 per unit; Grade-C model is sold at $450 per unit. XYZ requires 25lb of steel and 5 labor hours to manufacture a Grade-A machine requires, 22lb of steel and 4 labor hours for a Grade-B machine, and 20lb of steel and 3 labor hours for a Grade-C machine. A total of 6000lb of steel and 1500 hours are available. If any Grade-A machine is produced, an equipment cost of $20,000 is incurred; if any Grade-B machine is produced, an equipment cost of $18,000 is incurred; if any Grade-C machine is produced, an equipment cost of $15,000 is incurred.
a) What is the effective capacity for each model of expresso machine, respectively?
b) In the optimal solution, which type(s) machine will be manufactured? What is the optimal production quantity? What is the optimal profit?
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