MSIS 311 Quiz January 27, 2018 Last Name VenPafal First Name Sram Ajax Fuels, In

Question

MSIS 311 Quiz January 27, 2018 Last Name VenPafal First Name Sram 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:0 ounces per gallon of fuel. The mix or blend of the three ingredients is critical. At least one ounce of ingredient A must be used for every ounce of ingredient 8. The amount of ingredient c must be at least one-half the amount of ingredient A. If the cost of ingredients A, B and C are $0.10, $0. 03, and $0.09, respectively. find the minimum-cost mixture of A, 8, and C for each gallon of airplane fuel. Create a linear mathematical model for this problem in the form of a linear programming problem, stating the variables, the objective function and the constraints. Do not attempt to solve it.

Explanation / Answer

Objective function :

Let the corresponding quantities of three ingredients for each Gallon of fuel as follows :

Quantity of ingredient A = Ia

Quantity of ingredient B = Ib

Quantity of ingredient C = Ic

Ia, Ib, IC > = 0

The costs of above three ingredients A, B, C are $0.10 , $0.03 and $0.09 per unit

Therefore , total cost of ingredients per Gallon of fuel , $

= 0.10 x Ia + 0.03xIb + 0.09x Ic

Since the objective is to find the minimum cost mixture,

The objective function = Z = Minimize ( 0.1.Ia + 0.03.Ib + 0.09.Lb)

Constraints :

a)Since total amount of additives must be at least zero ounces per gallon of fuel :

Ia + Ib + Ic > = 0

b)At least one ounce of ingredient A must be used for 1 ounce of ingredient B :

Therefore ,

Ia>= Ib

Or, Ia – Ib > = 0

c)Amount of ingredient C must be one half of ingredient A .

Therefore , Ic > = ½ x Ia

Or, Ic – 1/2xIa > = 0

Or, Ic – 0.5xIa > = 0

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