Chloe is buying souvenirs on vacation. She wants to spend $70 at the most but only has 60 cubic inches of space available in her luggage.
if bracelets cost $7 and take up 3 in3 of space and t-shirts are $5 but take 15 in3 of space, write and graph a system of four inequalities thatmodel Chloe's possible purchases. letx= number of bracelets and y= number of t-shirts; use a scale of 2 on both axes.
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Let x represent the number of bracelets purchased, and let y represent the number of t-shirts purchased.
The following are the constraints, or the inequalities that restrict Chloe's choices:
(1) `x>= 0` since she cannot purchase a negative number of bracelets
(2) `y>= 0` for the same reason.
(3) The total amount Chloe will spend is found by taking the number of bracelets purchased (x) times 7, plus the number of t-shirts (y) times 5. The total spent must be less than or equal to 70 so
`7x+5y <= 70`
(4) The total amount of space used is found by taking the number of bracelets (x) times 3 cu inches each, plus the number of t-shirts (y) times 15 cu inches. The total amount of space must be less than or equal to 60 cu inches.
`3x+15y <= 60`
I cannot show the shading. You would shade only in the first quadrant, and only the side of both lines towards (0,0). You will have shaded only the small quadrilateral in the bottom left corner. This is the solution set (or feasible region).
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