Question

Eric's Carpentry manufactures two types of bookshelves that are 4 feet tall and 3 feet wide, a basic model and a deluxe model. Each basic bookshelf requires 1.5 hours for assembly and 1 hour for finishing; each deluxe model requires 2.5 hours for assembly and 1 hour for finishing. Two assemblers and one finisher are employed by the company and each works 40 hours per week. Eric can sell more basic models than deluxe models, so he wants the number of basic models produced to be 50% more than the number of deluxe models produced. If he makes $50 profit on the basic models and $65 profit on the deluxe models, how many should he make to maximize the profit? What is the maximum profit?
Please show all work! Will definitely upvote!

Answer 1

The maximum profit based on the equation given is $3300.

How to get the profit?

x = number of basic model

y = number of deluxe model

Since we hired 2 assemblers, we have to multiply the hours available by 2.

1.5 x + 2.5 y ≤ 40

Simplifying:

1.5 x + 2.5 y≤ 80

x+ y < 40

"If he makes $50 profit on the basic models and $65 profit on the deluxe models,"

Profit p = 50x + 65y.

The maximum value of x will be 40 and y = 20. Therefore, the profit will be:

= 50(40) + 65(20)

= 2000 + 1300

= 3300

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