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SpyIntel [72]
3 years ago
12

Ethan builds two different kinds of chairs, rockers and swivels. It takes him 3 hours to build a rocker and requires 2 oz of sta

in. It takes him 2 hours to build a swivel chair and requires 8 oz of stain. Ethan has 56 oz of stain available and he can only work up to 24 hours. He makes $12 profit on each rocker and $10 profit on each swivel chair. 1. Since there cannot be negative chairs, create two constraints to represent this. 2.Create a constraint for the hours it takes to build the chairs. 3. Create a constraint for the stain it takes for the chairs. PLEASE HELP
Mathematics
1 answer:
Angelina_Jolie [31]3 years ago
8 0

Answer:

(1) x\geq 0\; \text {and}\;y\geq 0

(2) 3x + 2y\leq 24

(3) x+4y\leq 28

Step-by-step explanation:

Let x and y be the numbers of rockers and swivels made by Ethan.

(1) Since the number of chairs can't be negative. So,

x\geq0 and y\geq 0 are the two constraints.

(2) He can work a maximum of 24 hours.

The time required to make 1 rocker chair and 1 swivels chair are 3 hr and 2 hr respectively.

So, the time required to make x rocker chair = 3x hr

and the time required to make y swivel chair = 2y hr.

The total time required is  3x + 2y hr which can't be more than the available time, 24 hr.

So, the required constraint is

3x + 2y\leq 24

(3) Similarly,

As 1 rocker chair requires 2 oz strain and 1 swivel chair required 8 ox strain.

So, to make x rocker chair 2x oz required and make y swivel chair 8y oz required which can't be more than the available oz, 56.

So, the required constraint is

2x + 8y\leq 56

\Rightarrow x+4y\leq 28.

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