Problem 3-29 (Algorithmic) La Jolla Beverage Products is considering producing a wine cooler that would be a blend of a white wine, a ros wine, and fruit juice. To meet taste specifications, the wine cooler must consist of at least 45% white wine, at least 20% and no more than 35% rose, and exactly 25% fruit juice. La Jolla purchases the wine from local wineries and the fruit juice from a processing plant in San Francisco. For the current production period, 10000 gallons of white wine and 6500 gallons of ros wine can be purchased; an unlimited amount of fruit juice can be ordered. The costs for the wine are $1 per gallon for the white and $1.5 per gallon for the rose; the fruit juice can be purchased for $0.5 per gallon. La Jolla Beverage Products can sell all of the wine cooler it can produce for $3 per gallon. a. Is the cost of the wine and fruit juice a sunk cost or a relevant cost in this situation? Relevant cost because the cost has notalready been incurred b. Formulate a linear program to determine the blend of the three ingredients that will maximize the total profit contribution. Solve the linear program to determine the number of gallons of each ingredient La Jolla should purchase and the total profit contribution it will realize from this blend. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. Enter "O" if your answer is zero. If constant is "1",it must be entered in the box Let W-gallons of white wine Let R-gallons of rose wine et F-nallons of fruit wine