Develop a Linear Programming model with explanations.
Ajax Fuels, Inc., is developing a new additive for airplane fuels. The additive is a mixture of three ingredients: A, B, and C. For proper performance, the total amount of additive (amount of A + amount of B + amount of C) must be at least 10 ounces per gallon of fuel. However, because of safety reasons, the amount of additive must not exceed 15 ounces per gallon of fuel. The mix or blend of the three ingredients is critical. At least 1 ounce of ingredient A must be used for every ounce of ingredient B. The amount of ingredient C must be greater than one-half the amount of ingredient A. If the costs per ounce for ingredients A, B, and C are $0.10, $0.03 and $0.09, respectively, develop the LP model that could be used to solve this problem for the minimum cost mixture of A, B, and C for each gallon of airplane fuel.
Let the optimum mix have x ounces of A, y ounces of B and z ounces of C.
A Complete, Neat and Step-by-step Solution is provided.