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------------------------------------------------ Soundex produces two models of satellite radios. Model A requires 15 minutes of work on Assembly Line I and 10 minutes of work on Assembly Line II. Model B requires 10 minutes of work on Assembly Line I and 12 minutes of work on Assembly Line II. At most, 25 labor-hours of assembly time on Line I and 22 labor-hours of assembly time on Line II are available each day. It is anticipated that Soundex will realize a profit of $12 on Model A and $10 on Model B. How many satellite radios of each model should be produced each day to maximize Soundex's profit?

A. 60 A and 60 B
B. 60 A and 100 B
C. 190 A and 0 B
D. 50 A and 70 B

This question requires linear programming to figure out how many of each model radios, A and B, should be produced each day to maximize profit while considering the constraints of labor hours available on assembly lines I and II.

This is a linear programming problem. We need to maximize the profit of Soundex while being cognizant of the labor hours available on each assembly line. Thus, we will set up and solve a system of inequalities.

A as the number of Model A radios

B as the number of Model B radios

Each model A radio requires 15 minutes of work which is 0.25 hours, and each model B radio requires 10 minutes which is around 0.167 hours. The total hours should be less than or equal to 25 for line I. Our first equation is:

0.25A + 0.167B ≤ 25

For line II, each model A radio requires 10 minutes or about 0.167 hours and each model B radio 0.2 hours. The total hours should be less than or equal to 22. Our second equation is:

0.167A + 0.2B ≤ 22

The objective is to maximize profit for Soundex. The amount of profit for each model A radio is $12, and for each model B radio is $10. We can represent it as:

P = 12A + 10B

You would solve these equations using graphical method or use software for linear programming to get the number of Model A and Model B radios that maximize the profit while considering the constraints.

Learn more about the topic of Linear Programming here:

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