La Jolla Beverage Products is considering producing a winecooler that would be a blend of a white wine, a rose wine, andfruit juice. To meet taste specifications, the wine cooler mustconsist of at least 50% white wine, at least 20% and no more than30% rose, and exactly 20% fruit juice. La Jolla purchases the winefrom local wineries and the fruit juice from a processing plant inSan Francisco. For the current production period, 10000 gallons ofwhite wine and 8000 gallons of rose wine can be purchased; anunlimited amount of fruit juice can be ordered. The costs for thewine are $1 per gallon for the white and $1.5 per gallon for therose; the fruit juice can be purchased for $0.5 per gallon. LaJolla Beverage Products can sell all of the wine cooler it canproduce for $2.5 per gallon.
a. Is the cost of the wine and fruit juice a sunk costor a relevant cost in this situation? Explain.
b. Formulate a linear program to determine the blend ofthe three ingredients that will maximize the total profitcontribution. Solve the linear program to determine the number ofgallons of each ingredient La Jolla should purchase and the totalprofit contribution it will realize from this blend. If required,round your answers to one decimal place. For subtractive ornegative numbers use a minus sign even if there is a + sign beforethe blank.
| Let W = gallons of white wine |
| Let R = gallons of rose wine |
| Let F = gallons of fruit wine |
| Max | __________W | + | _________R | + | __________F | | | |
| s.t. | | | | | | | | |
| __________W | + | __________R | + | __________F | ? | __________ | % white |
| __________W | + | __________R | + | __________F | ? | __________ | % rose minimum |
| __________W | + | __________R | + | __________F | ? | __________ | % rose maximum |
| __________W | + | __________R | + | __________F | = | __________ | % fruit juice |
| __________W | | | | | ? | __________ | Available white |
| | | __________R | | | ? | __________ | Available rose |
| W, R, F ? 0 |
| Optimal Solution: |
|---|
| W | __________ |
| R | __________ |
| F | __________ |
Profit Contribution = __________
c. If La Jolla could obtain additional amounts of thewhite wine, should it do so? YES OR NO
If so, how much should it be willing to pay for each additionalgallon, and how many additional gallons would it want topurchase?
d. If La Jolla Beverage Products could obtain additionalamounts of the rosé wine, should it do so? YES OR NO.
If so, how much should it be willing to pay for each additionalgallon, and how many additional gallons would it want topurchase?
e. Interpret the shadow price for the constraintcorresponding to the requirement that the wine cooler must containat least 50% white wine. What is your advice to management giventhis shadow price?
f. Interpret the shadow price for the constraintcorresponding to the requirement that the wine cooler must containexactly 20% fruit juice. What is your advice to management giventhis shadow price?
