Part II: Business Problem Solving using Excel $(40$ Points$)$

Problem $1.$ A shoe manufacturer produces four different products at their plan $($ballet shoe, climbing shoe, dress shoe, and fashion boot$).$ Production of each product requires three different kinds of raw material. Unit price, variable cost, and the bill of material $($the pound of raw material $1,$ the pound of raw material $2,$ and the pound of raw material $3,$ needed to produce each a product$)$ are as follows:

This month, $1600$ pounds of raw material $1,2500$ pounds of raw material $2,$ and $1100$ pounds of raw material $3$ are available. How can this shoe manufacturer maximize its monthly profit? Assuming, that the minimum demand of $100$ units for each type of shoe must be met.

Question $21(10$ points$).$ Build a mathematical model $($IPO model$)$ for the given optimization roblem.

Question $22(10$ points$).$ Has solver found an integer solution within tolerance. All constraints are tisfied? If yes, what is the optimal production mix?