Consider a company manufacturing two kinds of TV sets. A standard model and a de

Question

Consider a company manufacturing two kinds of TV sets. A standard model and a deluxe model. Suppose the number of hours of labor needed to produce the standard model is 13 hours/set while the number of hours to produce the deluxe model is 19 hours/set. Suppose further that the company has a total of 390 hours of labor available per week and the company's capacity is 25 sets per week. How many standard and how many deluxe sets should the company produce to fully utilize the hours and capacity available?

Explanation / Answer

Let the standard model produced are s and deluxe models are d

13s + 19d <= 390

s + d <= 25

to fully utilize both hours and capacity

13s + 19d = 390

s + d = 25

multiply equation2 by 13 and subtract from equation1

6d = 390 - 25*13 = 325 = 65

d = 65/6 = 11

s = 85/6 = 14

with 14 standard model and 11 deluxe model, total labor hours = 14*13+11*19 = 391 hours

it excceds the labour hour by 1 hour. so it is not acceptable.

with 15 standard model and 10 deluxe model, total labor hours = 15*13+10*19 = 385 hours

so 15 standard model and 10 deluxe model is the answer.

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