2. A furniture manufacturer produces two types of display cabinets, type X and type Y. On a weekly basis he must produce at least 2 of each type, but not more than 5 of type X or more than 6 of type Y. It takes 4 hours to produce type X and 5 hours for type Y in a 40 hour working week. At least 12 workers are needed with 2 working on type X and 3 on type Y at any one time. 2.1 Represent the above information as a system of inequalities. 2.2 Draw a graph of the system and indicate the feasible region clearly. 2.3 If the profit (P) on type X is R800 and on type Y is R1000, write down the objective function in the form P= ax + by. 2.4 Determine the number of each type that must be produced each week to make a maximum profit. Determine the maximum profit.

Understanding Business
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ISBN:9781259929434
Author:William Nickels
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Chapter1: Taking Risks And Making Profits Within The Dynamic Business Environment
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2. A furniture manufacturer produces two types of display cabinets, type X and type Y. On a
weekly basis he must produce at least 2 of each type, but not more than 5 of type X or more
than 6 of type Y. It takes 4 hours to produce type X and 5 hours for type Y in a 40 hour
working week. At least 12 workers are needed with 2 working on type X and 3 on type Y at
any one time.
2.1 Represent the above information as a system of inequalities .
2.2 Draw a graph of the system and indicate the feasible region clearly.
2.3 If the profit (P) on type X is R800 and on type Y is R1000, write down the objective
function in the form P= ax + by .
2.4 Determine the number of each type that must be produced each week to make a
maximum profit. Determine the maximum profit.
Transcribed Image Text:2. A furniture manufacturer produces two types of display cabinets, type X and type Y. On a weekly basis he must produce at least 2 of each type, but not more than 5 of type X or more than 6 of type Y. It takes 4 hours to produce type X and 5 hours for type Y in a 40 hour working week. At least 12 workers are needed with 2 working on type X and 3 on type Y at any one time. 2.1 Represent the above information as a system of inequalities . 2.2 Draw a graph of the system and indicate the feasible region clearly. 2.3 If the profit (P) on type X is R800 and on type Y is R1000, write down the objective function in the form P= ax + by . 2.4 Determine the number of each type that must be produced each week to make a maximum profit. Determine the maximum profit.
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