Question

Chapter 03 Homework La Jolla Beverage Products is considering producing a wine cooler that would be a blend of a white wine, a rosé 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, 10,000 gallons of white wine and 8,000 gallons of rosé wine can be purchased; an unlimited amount of fruit juice can be ordered. The costs for the wine are $1.00 per gallon for the white and $1.50 per gallon for the rose; the fruit juice can be purchased for $0.50 per gallon La Jolla Beverage Products can sell all of the wine cooler it can produce for $2.50 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 not already 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 "0" if your answer is zero. If the constant is "1" it must be entered in the box. Let W = gallons of white wine Let R = gallons of rose wine Let F = gallons of fruit wine Type here to search

Answer 1

Refer to the below images for the above mentioned questions, in a detailed way of solution.

cm @ : Reapin Relevant cost purchase wine Since and Lajolla fruit juice Beverage on an products can as-needed basis. ent " Let w = R = F = gallons gallons galions of white wine of rose wine of froit juice Realurement B Max 15W or5w -Doaw & - + IR DJR 0.88 + F -05F -0.2f 20 l White zo 4. rose minimom -0.3W -0-2W + - 0.7R 0.22 -003F +0.8F Lol. rose maximum = o to trust juice [ 10000 Available white < 8000 Available rose W,R,F 20 solution: W = 10,000 contribution = $29000 R=6000, optimal profit F = 4000

@ Requirement Since the cost of the wine is a relevant cost the door price of $2.90 is the maximum premium (over the normal price of $9.00) that lajolla Beverage products should be willing to pay to obtain one additional gallon of white wine. In other words at a price of $3-90 = 12-got 81-00 the additional cost is exactly eala to the additional revenue. , Searte vement No gallons of the rose are currently only 6000 being used. -- - @ Reaju/rement Requiring 5610 plus one gallon of white wine would reduce profit by $2.40. Although this explanation is technically correct it does not provide an explanation that is especially useful in the context of the problem. Alternatively, we find it useful to explore the question of what would happen if the white wine requirement were changed to at least 5t. Note that in this case, the first constraint would change to 0049 W -0.5R-0.JIF zo. This shows the hand side are the scope of Resolving the will show the student that the Coefficients changing note that this sensitivity analysis discussed problem with this revised effect on profit of a on the left is beyond in this chapter. constraint to change.

: vixement Allowing by one the amount gallon will of fruit increase juice to exceed 204 profit by $1.00