Pots-R-Us obtains its stock of outdoor decorative pots from three suppliers. Eac

Question

Pots-R-Us obtains its stock of outdoor decorative pots from three suppliers. Each supplier sells pots in four sizes (large, medium, small and tiny) in the percentage quantities and prices given in the following table. Each Quarter Pots-R-Us places and order with each supplier. At least 100 large, 60 medium, 50 small and 40 tiny pots must be purchased each quarter in order to meet demand. Because the supplier facilities have limited production, at most 140 pots can be purchased from any supplier in any quarter. Formulate an LP (ignoring possible fractional number of pots issues) that can be used to minimize the cost of acquiring the needed pots for one quarter. Use appropriate software to find solutions. Describe your solution in terms of the problem description.

Explanation / Answer

Let X1, X2 & X3 be the number of pots bought in a quarter from supplier 1, 2 and 3 respectively.

Thus, X1, X2, X3 <= 140

For meeting the quarterly demands, equation for no. of large pots is given by:

0.35*X1 + 0.3*X2 + 0.1*X3 >= 100

For Medium pots:

0.4*X1 + 0.25*X2 + 0.1*X3 >= 60

For Small Pots:

0.15*X1 + 0.35*X2 + 0.5*X3 >=50

For tiny pots:

0.1*X1 + 0.1*X2 + 0.3*X3 >= 40

Also, the total cost of pots in a quarter is given by,

Z = 4*X1 + 3*X2 + 2*X3

So, the LP problem is given as below:

Minimize Z = 4*X1 + 3*X2 + 2*X3

Constraints:

0.35*X1 + 0.3*X2 + 0.1*X3 >= 100

0.4*X1 + 0.25*X2 + 0.1*X3 >= 60

0.15*X1 + 0.35*X2 + 0.5*X3 >=50

0.1*X1 + 0.1*X2 + 0.3*X3 >= 40

X1, X2, X3 <= 140

and X1, X2, X3 >= 0

By solving the above LP problem, we get

Z = 1160

X1 = 140, X2 = 140 & X3 = 90

Thus, 140 no. of pots from supplier 1, 140 no. of pots from supplier 2 and 90 of pots from supplier 3 to be bought to meet the quarterly demand with minimum cost of 1160.

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