company is developing a new addiftive for gasoline. The additive is a mixture of
ID: 3348628 • Letter: C
Question
company is developing a new addiftive for gasoline. The additive is a mixture of three liquid ingredients: I, II, and Ill For proper performance, the total amount of additive must be at least 10 unces per barrel of gasoline. However,for safety reasons, the amount of adslive should not exceed 15 ounces per barel of gasoline. Al least ounce of ingredient I must be used for every ounce of ingredient I1, and at least 1 ounce of ingredient lill must be used for every ounce of ingredient I. Iif the costs of I, II, and Ill are $0.40, $0.09, and $0.27 per ounce, respectively, use echnology to find the mixture of the three ingredients that produces the minimum cost of the additive. What is the minimum cost? The mixture ofounces of ingredient , ounces of ingredient i, and ounces of ingredient Ill produces the minimum cost of the aditive The minimum cost is s per barrel. (Round to the nearest cent as needed.)Explanation / Answer
Let the quantity of ingredients be x,y,z ounces respectively.
To minimize z= 0.40x + .09y + 0.27z
subject to
x+y+z>=10,
x+y+z<=15,
x>=(1/3)y => x- (1/3)y >=0,
z>=x => z-x=0,
x>=0,y>=0,z>=0.
Solving the above linear programming model, we get
Minimum cost= $1.22
Quantity of ingredient I for minimum cost= 2 ounces
Quantity of ingredient II for minimum cost= 6 ounces
Quantity of ingredient III for minimum cost= 2 ounces
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