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An online furniture store sells chairs for $200 each and tables for $650 each. Every

day, the store can ship a maximum of 45 pieces of furniture and must sell no less than
$16000 worth of chairs and tables. If a represents the number of tables sold and y
represents the number of chairs sold, write and solve a system of inequalities
graphically and determine one possible solution.

1 Answer

5 votes

Answer:

(a, y) = (10, 25)

Explanation:

The two constraints give rise to two inequalities: one for the maximum number of pieces shipped, and one for the minimum revenue. A solution is a point on the graph where the inequality solutions overlap.

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inequalities

We're told to use 'a' for the number of chairs, and 'y' for the number of tables.

a +y ≤ 45 . . . . . . the maximum number that can be shipped is 45

200a +650y ≥ 16000 . . . . . revenue must be at least 16000

graph

The line for the revenue equation has a slope of -200/650 = -4/13. The solution space is above this line.

The line for the quantity shipped equation has a slope of -1, somewhat steeper. The solution space is below this line.

The boundary lines combine to define a wedge-shaped solution area in the left part of the first quadrant. One point that can be found in that area is ...

(a, y) = (10, 25)

One possible solution is to sell 10 chairs and 25 tables.

An online furniture store sells chairs for $200 each and tables for $650 each. Every-example-1
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