Question

- HI JUMLU in Problem 497 Xara Stores in the United States imports the designer-inspired clothes it sells from suppliers in China and Brazil. Xara estimates that it will have 45 orders in a year, and it must arrange to transport orders (in less-than-full containers) by container ship with shippers in Hong Kong and Buenos Aires. The shippers Xara uses have a travel time of 32 days from Buenos Aires and 14 days from Hong Kong, and Xara wants its orders to have an average travel time of no more than 21 days. About 10% of the annual orders from the shipper in Hong Kong are damaged, and the shipper in Buenos Aires damages about 4% of all orders annually. Xara wants to receive no more than 6 damaged orders each year. Xara does not want to be dependent on suppliers from just one country, so it wants to receive at least 25% of its orders from each country. It costs $3,700 per order from China and $5,100 per order to ship from Brazil. Xara wants to know how many orders it should ship from each port in order to minimize shipping costs. a. Formulate a linear programming model for this problem. h. Solye this model by using granhical analysis

Answer 1

a.

Let 'C' and 'B' represents the number of order to be placed to the suppliers of China and Brazil respectively.

Minimize Z = 3700 C + 5100 B

Subject to,

C + B = 45

14 C + 32 B <= 21 (C + B) or, -7 C + 11 B <= 0

0.10 C + 0.04 B <= 6

C >= 45*25% i.e. 11.25

B >= 45*25% i.e. 11.25

C, B >= 0

b.

-C + B = 45 --7 C + 11 B <= 0 0.10 C+0.04 B <= 6 C>= 11.25 B >= 11.25 V 20 40 60 80 100

The feasibility region is just the line segment XY which consists of two corner points X and Y.

So,

Evaluate these two points to find where the objective is minimized:

Point	C	B	Z = 3700 C + 5100 B
X	27.5	17.5	191000
Y	33.75	11.25	182250 (min)

So, the optimal solution is C = 33.75 and B = 11.25 with Max Z = 182,250