Question

La Jolla Beverage Products is considering producing a wine cooler that would be a blend of a white wine, a rose wine, and fruit juice. To meet taste specifications, the wine cooler must consist of at least 50% white wine, at least 20% and no more than 30% rose, and exactly 20% 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, 11000 gallons of white wine and 6500 gallons of rose 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? Sunk cost or Relevent Cost. Explain Why?

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. If required, round your answers to one decimal place. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank.

	Let W = gallons of white wine
	Let R = gallons of rose wine
	Let F = gallons of fruit wine

ax	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 the white wine, should it do so? YES or NO If so, how much should it be willing to pay for each additional gallon, and how many additional gallons would it want to purchase?

d.If La Jolla Beverage Products could obtain additional amounts of the rosé wine, should it do so? YES or NO If so, how much should it be willing to pay for each additional gallon, and how many additional gallons would it want to purchase?

e. Interpret the shadow price for the constraint corresponding to the requirement that the wine cooler must contain at least 50% white wine. What is your advice to management given this shadow price?

Answer 1

M AB D E F G H I J K L 1 La Jolla Beverage Products is considering producing a wine cooler that would be a blend of a white wine, a rose wine, and fruit juice. 2 To meet taste specifications, the wine cooler must consist of at least 50% white wine, at least 20% and no more than 30% rose, and exactly 20% fruit juice. 3 La Jolla purchases the wine from local wineries and the fruit juice from a processing plant in San Francisco. For the current production period, 4 11000 gallons of white wine and 6500 gallons of rose wine can be purchased: an unlimited amount of fruit juice can be ordered. The costs for the wine are 5 $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 6 of the wine cooler it can produce for $3 per gallon. 7 (a) Is the cost of the wine and fruit juice a sunk cost or a relevant cost in this situation? Sunk cost or Relevent Cost. Explain Why? Ans.: Relevant cost since LaJolla Beverage Products can purchase wine and fruit juice on an as - needed basis. 11 (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. If required, round your answers to one decimal place. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. Ans.: Let W = gallons of white wine Let R=gallons of rose wine Let F = gallons of fruit wine

H J Rectangularak Maximize P=2W +1.5R+2.5F Subject to: 0.5W -0.5R-0.5F 20 (Constraints for % white) -0.2W +0.8R-0.2F 20 (Constraints for % rose minimum) -0.3W +0.7R-0.3F 50 (Constraints for %rose maximum) -0.26 -0.2R+0.8F-0 (Constraints for % fruit juice) W S11000 Available white) R$6500 Available rose) WR, F20 Profit Optimal Solution: $2.0 White wine $1.5 Rose wine $2.5 Fruit wine Max Profit Capacity 11000 11000 6500 4375 $42,687.50 6500 4375 S42,687.50 Profit Contribution = 0.5 -0.5 -0.2 Decision variable Constraints % white % rose minimum % rose maximum % fruit juice Available white Available rose -0.5 0.8 0.7 -0.2 -0.3 62.5 2125 -62.5 0 11000 6500 -0.2 -0.3 0.8 0 0 -0.2 0 0 11000 6500