solvent base produced.

RMC$\text{'}$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:

$\backslash$table$[[$Raw Material,Amount Available for Production$],[$Material $1,38$ tons$],[$Material $2,10$ tons$],[$Material $3,39$ tons$]]$

Assuming that RMC is interested in maximizing the total profit contribution, answer the following. $($Assume $F$ is the number of tons of fuel additive and $S$ is the number of tons of solvent base.$)$

$($a$)$ What is the linear programming model for this problem that maximizes profit $($in dollars$)?$

Max $$

s$.$t$.$

Material $1$

Material $2$

Material $3$

$F,S0$

$($b$)$ Find the optimal solution using the graphical solution procedure. How many tons of each product should be produced?

$(F,S)=$

What is the projected total profit contribution $($in dollars$)?$

$$

$($c$)$ Is there any unused material? If so$,$ how much $($in tons$)?($If there is no unused material, enter $0.)$

Material $1q,$ tons

Material $2q,$ tons

Material $$ tons

$($d$)$ Are any of the constraints redundant? If so$,$ which ones? $($Select all that apply.$)$

Material $1$ constraint

Material $2$ constraint

$-$Material $3$ constraint

No redundant constraints

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