Q$1$ For the linear program

Max $2$A$+3$B

s$.$t

$1$A$+2$B$<=6$

$5$A$+3$B$<=15$

A$,$B$>=0$

Find the optimal solution using the graphical solution procedure. What is the value of the object function at the optimal solution?

Q$2$ RMC$,$ Inc., is a small firm that produces a variety of chemical products. In a particular production process, three raw materials are blended $($mixed together$)$ to produce two products: a fuel additive and a solvent base. Each ton of fuel additive is a mixture of $2/5$ ton of material $1$ and $3/5$ of material $3.$ A ton of solvent base is a mixture of $1/2$ ton of material $1,1/5$ ton of material $2,$ and $3/10$ ton of material $3.$ After deducting relevant costs, the profit contribution is $$40$ for every ton of fuel additive produced and $$30$ for every ton of solvent base produced. RMC$$s production is constrained by a limited availability of the three raw materials. For the current production period, RMC has available the following quantities of each raw material:

Raw Material Amount Available for Production

Material $120$ Tons

Material $25$ Tons

Material $321$ Tons

Assuming that RMC is interested in maximizing the total profit contribution, answer the following:

a$.$ What is the linear programming model for this problem?

b$.$ Find the optimal solution using the graphical solution procedure. How many tons of each product should be produced, and what is the projected total profit contribution?

c$.$ Is there any unused material? If so$,$ how much?

d$.$ Are any of the constraints redundant? If so$,$ which ones?

Need solution on excel thank you