It\'s a transportation model problem. The question is in the photo. Onenote Co.

Question

It's a transportation model problem. The question is in the photo.

Onenote Co. produces a single product at three plants sh au 1-6. The tomers. The three plants will produce 60, 80, and 40 respectively, during the next time period. The firm has made to sell 40 units to customer 1,60 units to customer customer 3. Both customers 3 and 4 also remaining units as possible. The net profit associated with shipping a unit from plant i for sale to cus- , and at least 20 units to want to buy as many of the tomer j is given by the following table: Customer 2 3 4 $700 500 $20 300 $800 500 600 100 300 Plant 2 200 400 500 wishes to know how many units to sell to customers Mnd how many units to ship from each of the plants to each 3 and 4 and unit of the customers to maximize profit. a) Formulate this problem as a trans portation problem where the objective function is to be maximized by constructing the appropriate parameter table that gives unit profits. (b )Now formulate this transportation problem with the usual ective of minimizing total cost by converting the param- obj eter table from part (a) into one that gives unit costs instead of unit profits.

Explanation / Answer

(a)

Objective function: Maximize Z = Total profit (in '00 $)
Z = 8X11 + 7X12 + 5X13 + 2X14 + 5X21 + 2X22 + 1X23 + 3X24 + 6X31 + 4X32 + 3X33 + 5X34

Subject to,

i Xi1 = 40
i Xi2 = 60
i Xi3 20
i Xi4 0

j X1j = 60
j X2j = 80
j X3j = 40

Xij 0; i=1,2,3 and j=1,2,3,4

(b)

Objective function: Minimize W = Total cost (in '00 $)
W = 8X11 + 7X12 + 5X13 + 2X14 + 5X21 + 2X22 + 1X23 + 3X24 + 6X31 + 4X32 + 3X33 + 5X34

Subject to,

i Xi1 = 40
i Xi2 = 60
i Xi3 20
i Xi4 0

j X1j = 60
j X2j = 80
j X3j = 40

Xij 0; i=1,2,3 and j=1,2,3,4

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