A Company Manufactures Two Models of Inline Skates,Alpha and Beta,at

Essay

A company manufactures two models of inline skates,Alpha and Beta,at two different manufacturing plants.The maximum output at plant I is 1000 per month,while the maximum output at plant II is 1200 per month.Due to contractual obligations,the number of Alpha models produced at plant I must exceed the number of Beta models produced at plant I by at least 100.The profit per Alpha and Beta model manufactured at plant I is $50 and $80,respectively,while the profit per Alpha and Beta model manufactured at plant II is $60 and $70,respectively.This month,the company received an order for 900 Alpha and 1000 Beta models.Find how many of each model should be produced at each plant in order to satisfy the order and maximize the profit.(Hint: Let
represent the number of Alpha models and
represent the number of Beta models manufactured at plant I.)