In: Accounting
Krappy Kraft Beer Inc. has two breweries in BC, with monthly capacities and production costs as follows:
Brewery 1: Capacity/month = 10,000 six-packs; Cost per six-pack = $1.60
Brewery 2: Capacity/month = 9500 six-packs; Cost per six-pack = $1.80
The product is channeled through 4 different distributors. Bart’s Beer is so popular that all stock that can be brewed is quickly purchased by the distributors, but the distributors can only handle a certain amount of product per month. Also, each distributor is willing to pay a different amount per six-pack to Bart:
Distributor Capacity/month
Distributor A: Capacity/month = 8500; Price per six-pack = $10.75
Distributor B: Capacity/month = 4500; Price per six-pack = $9.95
Distributor C: Capacity/month = 5500; Price per six-pack = $11.00
Distributor D: Capacity/month = 6500; Price per six-pack = $10.50
Bart’s Beer Inc. has to pay the cost of shipping to the 4
distributors. The shipping cost per six-pack from the breweries to
distributors is as follows:
Brewery 1: A = $1.00; B = $1.15; C = $1.85; D = $2.00
Brewery 2: A = $0.65; B = $.75; C = $1.50; D = $1.75
Formulate an LP model that will enable Bart’s Beer to maximize its profits each month.
Complete the following:
a) Develop the Transportation Network.
b) Formulate the problem into proper LP format.
c) Use Solver to determine the optimal solution. State the optimal solution in the context of the business
problem.
Objective Function (Z) = Profit = Revenue - Production Cost - Transportation Costs
Variables = Production shipped to each distributor
Revenue = Sales to each distributor x Price
Production Cost = Production at Brewery 1 x 1.6 + Production at Brewery 2 x 1.8
Transportation Cost = Product shipped to each location x transportaiton cost
Following is the snapshot of the excel I created for the problem
Brewery | A | B | C | D | ||||
1 | 10000 | 1.60 | 8500 | 4500 | 5500 | 6500 | ||
2 | 9500 | 1.80 | 10.75 | 9.95 | 11.00 | 10.50 | ||
Sales | A | B | C | D | ||||
1 | 5443 | 0 | 3557 | 1000 | 10000 | |||
2 | 3057 | 4500 | 1943 | 0 | 9500 | |||
8500 | 4500 | 5500 | 1000 | |||||
Revenue | 207150 | |||||||
Tpt Cost | ||||||||
1 | 1.00 | 1.15 | 1.85 | 2.00 | 14,023 | |||
2 | 0.65 | 0.75 | 1.50 | 1.75 | 8,277 | |||
Prod Cost | ||||||||
1 | 16000 | |||||||
2 | 17100 | |||||||
Profit | 151750 | |||||||
The optimal solution is as given below
Sales | A | B | C | D | |
1 | 5443 | 0 | 3557 | 1000 | 10000 |
2 | 3057 | 4500 | 1943 | 0 | 9500 |
8500 | 4500 | 5500 | 1000 |
The interpretation is that Brewery 1 should make 10000 units and ship 5443 to A, 3557 to B and 1000 to D. Similar it goes for Brewery 2 as well
Answer Report
Cell | Name | Original Value | Final Value | ||
$F$18 | Profit A | 151750 | 151750 | ||
Cell | Name | Original Value | Final Value | Integer | |
$F$7 | A | 5443 | 5443 | Integer | |
$G$7 | B | 0 | 0 | Integer | |
$H$7 | C | 3557 | 3557 | Integer | |
$I$7 | D | 1000 | 1000 | Integer | |
$F$8 | A | 3057 | 3057 | Integer | |
$G$8 | B | 4500 | 4500 | Integer | |
$H$8 | C | 1943 | 1943 | Integer | |
$I$8 | D | 0 | 0 | Integer | |
Cell | Name | Cell Value | Formula | Status | Slack |
$F$9 | A | 8500 | $F$9<=$F$3 | Binding | 0 |
$G$9 | B | 4500 | $G$9<=$G$3 | Binding | 0 |
$H$9 | C | 5500 | $H$9<=$H$3 | Binding | 0 |
$I$9 | D | 1000 | $I$9<=$I$3 | Not Binding | 5500 |
$J$7 | 10000 | $J$7<=$C$3 | Binding | 0 | |
$J$8 | 9500 | $J$8<=$C$4 | Binding | 0 | |
$F$7=Integer | |||||
$F$8=Integer | |||||
$G$7=Integer | |||||
$G$8=Integer | |||||
$H$7=Integer | |||||
$H$8=Integer | |||||
$I$7=Integer | |||||
$I$8=Integer |
I am not getting Sensitivyt report. However, I can answer the questions
i) Interpret the meaning of the shadow price for the monthly production capacity limitation of Brewery #2
Shadow price means that by chancing the capacity by 1 units, how much will the ouput change by
ii. Interpret the meaning of the reduced cost for shipping six-packs from Brewery 1 to Distributor D. (2 marks)
By reducing the cost of shipping from Brewery 1 to D, we can increase the product shipped to D instead of B as D is getting more profit than B
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