Question

Zen Inc. manufactures two types of products, the G1 and the T1 model airplane. The manufacturing process consists of two principal departments: production and assembly. The production department has 58 skilled workers, each of whom works 7 hours per day. The assembly department has 25 workers, who also work 7-hour shifts. On an average, to produce a G1 model, Zen Inc. requires 3.5 labor hours for production and 2 labor hours for assembly. The T1 model requires 4 labor hours for production and 1.5 labor hours in assembly. The company anticipates selling at least 1.5 times as many T1 models as G1 models. The company operates five days per week and makes a net profit of $130 on the G1 model, and $150 on the T1 model. Zen Inc. wants to determine how many of each model should be produced on a weekly basis to maximize net profit.

If the numbers of G1 and T1 products produced each week are denoted as G and T respectively, the function that describes the assembly’s department's labor constraint for a week is

Select one:

a. 6G + 8T ≤ 1620.

b. 2G + 4T ≥ 175.

c. 2G + 1.5T ≤ 875.

d. 3G + 4T ≥ 875.

Answer 1

Here,

It is a problem of Linear Programming,

where the numbers of G1 and T1 products produced each week are denoted as G and T respectively,

So, we have to find the function that describes the assembly’s department's labor constraint for a week.

In the question we are given there are a total of 25 workers in the assembly department.

Each of them works for 7 hours shift.

Therefore, the total hours of working for all 25 workers = (working hours for a single day)

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Now, we are given that for the G1 model, it requires 2 labor hours, therefore

Total hours required for G (number of G1 produced) = 2G ---------------------------------------------(this should be noted)

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Now, we are given that for T1 model it requires 1.5 labor hours, therefore

Total hours required for T (number of T1 produced) = 1.5T ---------------------------------------------(this should be noted)

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Now, we have to find labor constraints for a week and it is given that the company operates 5 days a week

Hence, total labor hours for a week = ---------------------------------------------(this should be noted)

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Therefore, the assembly's department's labor constraints would be

The correct answer is (C).

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