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BRICKS Problem A construction company with four warehouses needs a large supply of BRICKS on a monthly basis to each of the warehouses. The company has three different offers from brick manufacturers. The table below shows the overall price per 100 bricks from each manufactrurer delivered to each warehouse. The table also shows the requirements for each warehouse and the maximum order size from each manufaturer to a warehouse. This maximum order size means that for example, manufacturer 1 could supply maximum 2500 bricks to each of the warehouses. Also, the company does not want to buy more that 5000 bricks in total from a single manufacturer. The company wants to determine the number of bricks to buy from eachof the manufacturers in order to exactly satisfy the total requirement of each warehouse and minimize the total cost. The solution to this problem is called Plan A. Warehouse 1Warehouse 2Warehouse 3Warehouse 4Max Order Size Manufacturer 1 $50 Manufacturer 2 $48 Manufacturer 3 $47 Total Requirement 2000 $45 $48 $51 3000 $48 $51 $50 3500 $48 $54 $50 1500 2500 3000 2000 After presenting Plan A to the company, they are told that now manufacturer 1 charges a fixed fee of $10 per order. Also, they know that manufacturer 3 cannot supply more than two orders. The solution to this modified problem is called Plan BI know the answer of Plan A but don't know about Plan B. Please solve Plan B

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Answer #1

Plan A

B16 Q fx -SUMPRODUCT(B2:E4, B10:E12)/100 Max Order sizeS Solver Para W/h 1W/h 2 w/h3W/h 4 Capacity 48 51 2 Manufacturer 1 3 Manufacturer 2 4 Manufacturer 3 5 Demand 45 48 51 3000 48 2500 48 47 5000 3000 Set Objective: To: By Changing Variable Cells: SBS10:SES12 Subject to the Constraints: SBS13:SES13 SBS5:SES5 SFS10:SFS12SFS2:SFS4 SB510:SES10<-SGS2 SBS11:SES11 SGS3 SBS12 SES12SGS4 50 5000 Max Min O Value Of: 0 3500 1500 8 Optimal distribution plan W/h1 W/h2w/h3W/h4 Row Total Add 10 Manufacturer 1 11 Manufacturer2 12 Manufacturer3 13 Column Total 14 2500 500 1500 1000 5000 2000 2000 2000 3500 500 1500 4500 Delete Reset All Make Unconstrained Variables Non-Negative 16 Total Cost 17 18 19 4755 Select a Solving Method: Simplex LP Options Solving Method Select the IPOPT Nonlinear engine for Solver Problems that are smooth nonlinear.Sele the LP Simplex engine for linear Solver Problems. 21 Close 25 26

Formulas:

Cell Formula Copy to
F10 =SUM(B10:E10) F10:F12
B13 =SUM(B10:B12) B13:E13
B16 =SUMPRODUCT(B2:E4,B10:E12)/100

Total cost of plan A = 4755

Plan B

Formulas:

Cell Formula Copy to
F9 =SUM(B9:E9) F9:F11
B12 =SUM(B9:B11) B12:E12
F16 =SUM(B16:E16) F16:F18
B21 =B16*$G2-B9 B21:E23
B25 =SUMPRODUCT(B2:E4,B9:E11)/100+F16*10

Total cost of plan B = 4785

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