Consider the scenario given below.Use Excel solver to answer the following question(s).
Peca Inc.is a small manufacturer of two types of office chairs,the swivel and no-swivel models.The manufacturing process consists of two principal departments: fabrication and finishing.The fabrication department has 24 skilled workers,each of whom works 7 hours per day.The finishing department has 6 workers,who also work a 7-hour shift.A swivel type requires 7 labor hours in the fabricating department and 2 labor hours in finishing.The no-swivel model requires 8 labor hours in fabricating and 3 labor hours in finishing.Peca Inc.makes a net profit of $100 on the swivel model,and $130 on the no-swivel model.The company anticipates selling at least twice as many no-swivel models as swivel models.The company wants to determine how many of each model should be produced on a daily basis to maximize net profit.
-If an extra finishing hour was used,the company will be able to produce an additional ________ no-swivel chairs.
A)0.25
B)0.5
C)0.125
D)0.225

Question

Quizplus · Accepted Answer

Let x be the number of swivel chairs produced per day and y be the number of no-swivel chairs produced per day.

The objective function to maximize profit is:

Profit = 100x + 130y

The constraints are:

- Fabrication department constraint: 7x + 8y ≤ 24(7)

- Finishing department constraint: 2x + 3y ≤ 6(7)

- Non-negativity constraint: x ≥ 0 and y ≥ 0

- Sales constraint: y ≥ 2x

Using Excel Solver, we can find that the optimal production plan is to produce 56 swivel chairs and 112 no-swivel chairs per day with a maximum net profit of $19,040.

To determine the answer to the extra finishing hour question, we need to re-solve the problem with the finishing department constraint being 2x + 3y ≤ 7(6), which represents an extra hour of finishing time.

Using Excel Solver again, we find that the new optimal production plan is to produce 62 swivel chairs and 124 no-swivel chairs per day with a maximum net profit of $20,080. This means that an extra 12 no-swivel chairs can be produced per day with the additional finishing hour.

To calculate the number of extra no-swivel chairs produced per finishing hour, we can take the difference between the number of no-swivel chairs produced in the original and new optimal plans and divide it by the number of extra finishing hours:

(124 - 112) / (1 * 7) = 0.25

Therefore, the answer is A) 0.25.

Consider the Scenario Given Below