AMC, Inc, is a smail firm that produces a variefy of chemical products. In a particular production process, three raw materials are blended (mixed tosethery to produce two produme a fuce odtrittye and a solvent base, Each ton of fuel additwe 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 tan of material 1 , tis ton of material 2 , And 1/10 ton of material 3. After deducting relevant costs, the profit contribution is $40 for every ton of fuel additive produced and s3o for every ton of solvent base produced. RMCis production is constrained by a limited availability of the three raw maserisis. For the current production period, RMC has wralable the follewing eaantites of asch rais matenal: Assuming that AMC is interested in maximizing the total prent contributiod, answer the following. (Assume F is the number of tons of huel additive ans 5 is the fwimber ef thins of saverk base) (a) What is the linear programming model for this problem that maximires broda (in dollan)? Max Material 2 Material 3 F,S0 Material 251S10 Material 3 FsS0 (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.) \begin{tabular}{ll} Material 1 & tons \\ \hline Material 2 & tons \\ \hline Material 3 & tons \end{tabular} (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