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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.

User Nattrass
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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

User Gerben Jacobs
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