An Introduction to Management Science 13th Edition by David Anderson,Dennis Sweeney ,Thomas Williams ,Jeffrey Camm, Kipp Martin

Exercise 59

RMC, Inc., is a small firm that procedures a variety of chemical procedures. 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 ? ton of material 1 and ? of material 3. A ton of solvent bas is mixture of ½ ton of material 1, ? ton of material 2, and 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:
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, which ones?
d. Are any of the constraints redundant? If so, which ones?