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You are the operations manager of Spartan Ice Cream Shoppe that produces its own ice cream. You make and sell five favors; Vanila $($v$).$

Chocolate $($C$),$ Pistachio $($p$),$ Banana $($b$),$ and Rocky Road $($ir$).$ You want to make as much profit as you can, of course. The profits per gallon for the five flavors are Vanilla: $$140,$ Chocolate: $$175,$ Pistachio: $$170,$ Banana: $$125$ and Rocky Road: S$160.$ You can make up to $260$ gallons. You have to make at least $15$ gallons of each flavor and you cannot make more than $80$ gallons of any one flavor. Assume you sell all of the ice creams you make.

$$What objective are you trying to optimize $($cost$,$ profit, ice cream, or gallon$)?(1$ pt$)($Instruction: provide your answer exactly as the bold words$)$ Blank $1$

$$Are you maximizing, minimizing, or hitting a target for that objective? $(1$ pt$)($provide your answer exactly as the bold words$)$ Blank $2$

$$What is$/$are the decision variable$($s$)?(2$ pts$)($provide your answer in the format of $*$Xi $=$ the number of $***$ of $**)$ Blank $3$

$$What is$/$are the input variables $($e$.$g$.$: parameter$/$coefficient values used in the objective function$)?(2$ pts$)$ Blank $4$

$$What is the formula for what you are trying to optimize? $(2$ pts$)($show your answer in the format of "objective $=$ aX$1+$ bx$2+-)$

Blank $5$

$$What is$/$are the constraint$($s$)?(2$ pts$)($please describe your constraint$)$ Blank $6$

$$What is$/$are the formula$($s$)$ for the constraint$($s$)?(2$ pts$)($please show the answer in the format of $"$aX$1+$ bX$2+.\_.=$ or $=$ value$*)$

Blank $7$

$8.$ What is the solution to this problem? $(2$ pts$)$ Blank $8$