Question

The Valley Wine Company produces two kinds of wine—Valley Nectar and Valley Red. The wines are produced from 64 tons of grapes the company has acquired this season. A 1000-gallon batch of Nectar requires 4 tons of grapes and a batch of Red requires 8 tons. However, production is limited by the availability of only 50 cubic yards of storage space for aging and 120 hours of processing time. A batch of each type of wine requires 5 cubic yards of storage space. The processing time for a batch of Nectar is 15 hours and the processing time for a batch of Red is 8 hours. Demand for the two types of wine is limited to 7 batches, each. The profit for a batch of Nectar is $9,000 and the profit for a batch of red is $12,000. The company wants to determine the number of 1,000--gallon batches of Nectar and Red to produce in order to maximize profit.

a. Formulate a linear programming model for this problem.

b. Use POM for windows to obtain the solutions list and results printouts for this problem.

c. Answer the questions below from the printouts you obtained in b above and submit both the printout and answers to the questions to Blackboard by the time and date specified.

1. How much is produced of each type of wine to maximize profits and what is the maximum profit?

2. How much of each type of resource is left over?

3. What is the value for an additional unit of each resource?

4. Over what ranges are the values in 3) above valid?

5. What is the profit-per-unit at which the production plan will change for each type of wine?

Answer 1

Marémize 9000 N +12000 R Constraints Grapes = 4N+8R =) 64 Yards - SHASR 50 Processing Time = 151.48R -)120 Demand Nectar - N s) 7 Red = R >>7 N. RO following is the queel sheet.

SUM X fx =SUMPRODUCT(B4:04,83:03) A A B C D E Profit -SUMPRODUCT(84:C4,83:03) 2 Nectar Red 3 DV 4 Profit 9,000 12,000 5 6 Constraints 7 Grapes 8 Yards 5 5 9 Processing Time 15 10 Demand - Nectar 11 Red 0000 0 50 OOO

SUM ex fx =SUMPRODUCT(B$3:C$3,17:07) A B C D E F G Nectar Red 2 3 DVD 4 Profit 9,000 12,000 Profit 5 6 Constraints Grapes 8 Yards 9 Processing Time 10 Demand - Nectar 11 Red 8) -SUMPRODUCT(B$3:C$3,87:07) 5 50 50 15 8 0 120 19

Solver Parameters Set Objective: $F$4 To: Max Min Value of: By Changing Variable Cells: $8$3:$C$3 Subject to the Constraints: $D$7:$D$11 <= $E$7:$E$11 Add Change Delete Reset All Load/Save V Make Unconstrained variables Non-Negative Select a Solving Method: Simplex LP Options Solving Method Select the GRG Nonlinear engine for Solver Problems that are smooth nonlinear. Select the LP Simplex engine for linear Solver Problems, and select the Evolutionary engine for Solver problems that are non-smooth. Help Solve close

DE Nectar Red 3 DV 4 Profit 9,000 12,000 Profit 108,000 64 4 8 64 5550 6 Constraints 7 Grapes 8 Yards 9 Processing Time 10 Demand - Nectar 11 Red 208/ 120

☺ 4 batch of Nectar wines and 6 batch of Red wine s Produced. ③ 12 procening hours is left over. & It would be o because no matter procening hours Se used the other constraints are binding. ② Since Et makes no sense in wring Processing hours, ranges do not matter. 6 The Profit will remain Same Rey $108,000 with the Precrease in the value of processing hours, ao wme