20 At a certain refinery the refining process requires the p

(20%) At a certain refinery, the refining process requires the production of at least two gallons of gasoline for each gallon of fuel oil. To meet the anticipated demands of winter, at least three million gallons of fuel oil a day will need to be produced. The demand for gasoline, on the other hand, is not more than 6.4 million gallons a day. If gasoline is selling for $1.90 per gallon and fuel oil sells for $1.50/gal, how much of each should be produced in order to maximize revenue? Setup the Linear Programing problem, both the objective function and constraints, but you don\'t have to solve the problem. 5.

Solution

let number of gallons of gasoline = x , number of gallon of fuel oil = y

the refining process requires atleast 2 gallons of gasoline for each gallon of fuel oil

2xy

atleast 3 million gallons of fuel oil need to be produced

y3000000

the demand for gasoline is not more than 6.4 million gallons a day

x6400000

revenue,R(x,y)=1.9x+1.5y

objective function is R(x,y) =1.9x+1.5y

maximise R(x,y) =1.9x+1.5y

such that

2xy

y3000000

x6400000