An aerospace company is developing a new fuel additive for c

An aerospace company is developing a new fuel additive for commercial airliners. The additive is composed of three ingredients: P, Q, and R. For peak performance, the total amount of additive must he at least 10 mL/L of fuel. For safety reasons, the sum of the highly flammable P and Q ingredients must not exceed 5 mL/L. In addition, the amount of the P ingredient must always be equal to or greater than the Q ingredient, while the R ingredient must be greater than half the Q ingredient. i. If the cost per mL for the ingredients P, Q and R is $0.10, $0.05. and $0.30, respectively, set up a linear programming problem in the standard form to minimize the cost mixture for each liter of fuel. ii. Solve the above problem with the simplex method and also via a software package.

Solution

P+Q+R <= 10

P <= 5

Q<=5

P >= Q

R >=1/2 Q

z = 0.1 P +0.05Q+0.3R