Answer :
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.
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