Question

A wine cooler that would be a blend of a white wine, a rose wine, and fruit juice will be produced. To meet taste specifications, the wine cooler must consist of at least 45% white wine, at least 15% and no more than 30% rose; fruit juice will be exactly 80% of rose wine. For the current production period, 10,000 gallons of white wine and 8000 gallons of rose wine can be purchased; an unlimited amount of fruit juice can be ordered. The costs for the wine are $1.50 per gallon for the white and $1.50 per gallon for the rose; the fruit juice can be purchased for $0.50 per gallon. All of the wine cooler produced can be sold for $2.50 per gallon. Please formulate an LP model to determine the blend of the three ingredients that will maximize the total profit contribution. Let W be the gallons of white wine, R be the gallons of rose wine, and F be the gallons of fruit juice.

Which of the following can be used to formulate “the wine cooler must consist of at least 15% Rose wine”?

A. R <= 15%(W+ R+ F)

B. -0.15W+ 0.85R -0.15F <= 0

C. R >= 15%(W+R+F)

D. 0.15W- 0.85R -0.15F >= 0

Answer 1

Maximization of Profit = Selling price*(W+R+F) - Cost of W*W - Cost of R*R - Cost of F*F = 2.5*(W+R+F) - 1.5*W - 1.5*R - 0.5*F = W + R + 2*F

Ans C

Rose wine 'R' must be at least 15% of the wine cooler which is sum of the three types W + R + F