b$.$ Mathematically formulate a linear optimization model.

$($Type integers or decimals. Do not round. Do not include the$$ $ symbol in your$$ answers.$)$

$$

Maximize

Minimize

$$

Number of shoes

Cost

Material used

Profit

equals$=$

enter your response here Upper M $1$M$1$plus$+$enter your response here Upper M $2$M$2$plus$+$enter your response here Upper M $3$M$3$

enter your response here Upper M $1$M$1$plus$+$enter your response here Upper M $2$M$2$plus$+$enter your response here Upper M $3$M$3$less than or equals$<=1$ comma $3001,300$

enter your response here Upper M $1$M$1$plus$+$enter your response here Upper M $2$M$2$plus$+$enter your response here Upper M $3$M$3$less than or equals$<=2$ comma $0002,000$

enter your response here Upper M $1$M$1$plus$+$enter your response here Upper M $2$M$2$plus$+$enter your response here Upper M $3$M$3$less than or equals$<=8$ comma $5008,500$

enter your response here Upper M $1$M$1$plus$+$enter your response here Upper M $2$M$2$plus$+$enter your response here Upper M $3$M$3$less than or equals$<=1$ comma $1001,100$

Upper M $1$M$1,$ Upper M $2$M$2,$ Upper M $3$M$3$

$$

greater than or equals$>=$

not equals!$=$

equals$=$

greater than$>$

$0$