Question

Suppose a shoe factory produces both low- grade and high-grade shoes. the factory produces atleast twice as many low-grade as high-grade shoes. the maximum possible production is 500 pairs of shoes. A dealer calls for delivery of atleast 100 high-grade pairs of shoes per day. suppose the operation makes a profit of 2.00 dollars per a pair of shoes on high-grade shoes and 1.00 dollar per pairs of shoes on low-grade shoes. How many pairs of shoes of each type should be produced for maximum profit ?Let X denote the number of high-grade shoes. Let Y denote the number of low-grade shoes. Please be fast and Give all steps my teacher needs it after an hour so please give answers in 3o minutes.

Answer 1

I will write an equation for each statement

the factory produces atleast twice as many low-grade as high-grade shoes.

`y\ge2x`

maximum possible production is 500 pairs of shoes.

`\begin{gathered} x+y=500 \\ y=500-x \end{gathered}`

where x is the number of high-grade shoes and y the number of Low-grade shoes

and replace on the first equation

`\begin{gathered} 500-x\ge2x \\ 500\ge2x+x \\ 500\ge3x \\ x\le(500)/(3)\approx166.66 \end{gathered}`

the value of x must be less than or equal to 166.6 but we must use whole numbers so it will be 166

now replace on

`x+y=500`

to find y

`\begin{gathered} 166+y=500 \\ y=500-166 \\ y=334 \end{gathered}`

suppose the operation makes a profit of 2.00 dollars per a pair of shoes on high-grade shoes and 1.00 dollar per pairs of shoes on low-grade shoes.

`2x+y=P`

where P is the profit

and replce x and y to find the value of the profit

`\begin{gathered} P=2(166)+334 \\ P=332+334 \\ p=666 \end{gathered}`

The maximun profit must be $666