A retail store sells two types of shoes, sneakers, and sandals. The store owner pays $8 for the sneakers and $14 for the sandals. The sneakers can be sold for $10 and the sandals can be sold for $17. The owner of the store estimates that she won't sell more than 200 shoes each month, and doesn't plan to invest more than $2,000 on the inventory of the shoes. Let x= the number of sneakers in stock, and y=the number of sandals in stock. 1) Write an inequality that represents the possible amount of shoes she can purchase each month. 2) Next, write an inequality that represents how many sneakers and sandals she has in stock each month. 3) After graphing the constraints, what are the coordinates of the four vertices? Round your answers to the nearest whole number. 4)Write an equation to show the profit she will make on sneakers and sandals. 5)If she sold the number of sneakers and sandals that could maximize her profit, what would her maximum profit be?

(1)

(2)

(3)From the graph, the coordinates of the four vertices are:

(4)Profit Function: P(x,y)=2x+3y

(5)Maximum profit =$467

Step-by-step explanation:

Let the number of sneakers in stock =x

Let the number of sandals in stock =y

(1)The owner of the store estimates that she won't sell more than 200 shoes each month. Therefore, an inequality that represents the possible amount of shoes she can purchase each month is:

(2)She does not plan to invest more than $2,000 on the inventory of the shoes.

The store owner pays $8 for the sneakers and $14 for the sandals.

Therefore, an inequality that represents how many sneakers and sandals she has in stock each month is:

(3)From the graph, the coordinates of the four vertices are:

(4)The sneakers can be sold for $10 and the sandals can be sold for $17.

Profit on one sneaker =$10-8=$2

Profit on one sandal =$17-14=$3

Profit Function: P(x,y)=2x+3y

(5)

At (0,143), Profit =2x+3y=2(0)+3(143)=$429

At (0,0), Profit =2x+3y=2(0)+3(0)=$0

At (133, 67), Profit =2x+3y=2(133)+3(67)=$467

At (200,0), , Profit =2x+3y=2(200)+3(0)=$400

Her maximum profit will be $467 when she sells 133 sneakers and 67 sandals.

mrbilldoesmath!

answer: a parabola

steps:

(x-1)(x+4)   = x(x+4) - 1(x+4) = (x^2 + 4x) - (x+4)

                = x^2 +4x -x -4   = x^2 +3x -4

which is a parabola

mrb

no solution exists the way you wrote the equation.