Randall grew up in Ohio but now lives in California. He knows that snow sucks and...

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Randall grew up in Ohio but now lives in California. He knowsthat snow sucks and makes driving a nightmare. His father, Douglas,owns a specialty cars dealership chain in Ohio. Douglas knows thatit is very hard to sell sports cars in the winter. So, they see abusiness opportunity where they can ship and sell Corvettes fromOhio to California in the winter. They can make a profit of $3,000per car sold. This year Doug has 57 Corvettes in his Columbusstore, 55 in Cincinnati store, and 20 in his Cleveland store.Randall is able to broker deals with California dealers: VetteMaxwill buy 25, BlingRide is committed to 30, Americana signs acontract for 20, and BoyToys will buy 45.
The associated shipping costs are as follows:
$
VetteMax
BlingRide
Americana
BoyToys
Columbus
560
744
777
480
Cincinnati
704
810
604
570
Cleveland
801
890
502
703
a. How many Corvettes does BoyToys get from Columbus?
b.What is the total shipping cost?
c.What is their NET profit?

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a BoyToys get 32 Corvettes from Columbus b Total Shipping cost is 71360 c A total of 120 Corvettes are shipped and each gives a profit of 3000 thus net profit 3000 120 360000 First we find a basic feasible solution using Voggels Approximation method also then optimal solution using MODI method TOTAL number of supply constraints 3 TOTAL number of demand constraints 4 Problem Table is VetteMax BlingeRide Americana BoyToys Supply Columbus 570 744 777 480 57 Cincinnati 704 810 604 570 55 Cleveland 801 890 502 703 20 Demand 25 30 20 45 Here Total Demand 120 is less than Total Supply 132 So We add a dummy demand constraint with 0 unit cost and with allocation 12 Now The modified table is VetteMax BlingeRide Americana BoyToys Ddummy Supply Columbus 570 744 777 480 0 57 Cincinnati 704 810 604 570 0 55 Cleveland 801 890 502 703 0 20 Demand 25 30 20 45 12 Table1 VetteMax BlingeRide Americana BoyToys Ddummy Supply Row Penalty Columbus 570 744 777 480 0 57 4804800 Cincinnati 704 810 604 570 0 55 5705700 Cleveland 801 890 502 703 0 20 5025020 Demand 25 30 20 45 12 Column Penalty 134704570 66810744 102604502 90570480 000 The maximum penalty 570 occurs in row Cincinnati The minimum cij in this row is c25 0 The maximum allocation in this cell is min5512 12 It satisfy demand of Ddummy and adjust the supply of Cincinnati from 55 to 43 55 12 43 Table2 VetteMax BlingeRide Americana BoyToys Ddummy Supply Row Penalty Columbus 570 744 777 480 0 57 90570480 Cincinnati 704 810 604 570 012 43 34604570 Cleveland 801 890 502 703 0 20 201703502 Demand 25 30 20 45 0 Column Penalty 134704570 66810744 See Answer

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$	VetteMax	BlingRide	Americana	BoyToys
Columbus	560	744	777	480
Cincinnati	704	810	604	570
Cleveland	801	890	502	703