Eric's Carpentry manufactures two types of bookshelves that are 4 feet tall and 3 feet wide, a basic model (x1) and a deluxe model (x2). 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. Using x1 to denote the number of basic bookcases and x2 to denote the number of deluxe bookcases, write a system of linear inequalities that describes the possible number of each model of bookcase that can be manufactured in a week.

x1 (1.5)+ x2(2.5) ≤ 80

(1)x1 + (1)x2 ≤ 40

Explanation:

Hi, we have to write a system of equations.

Since a basic model (x1) requires 1.5 hours for assembly, and a deluxe model requires 2.5 hours for assembly, the sum of both products must be equal or less than the assembler’s available hours per week (40).

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

x1 (1.5)+ x2(2.5) ≤ 40(2)

Simplifying:

x1 (1.5)+ x2(2.5) ≤ 80

Now, for the finishing is a similar process.

Since both models requires the same time for finishing (1), and there is only one finsisher.

(1)x1 + (1)x2 ≤ 40

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