Math Problem Solver

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 perorder from China and $5,100 per order to ship from Brazil. Xara wants to know how many orders

it should ship from each port to minimize shipping costs.

a. Formulate a linear programming model for this problem.

b. Solve this model by using graphical/mathematical analysis.

c. Now, the Chinese shipper would like to gain more shipping orders from Xara because

it’s a prestigious company and would enhance the shipper’s reputation. It has therefore made the

following proposals to Xara:

i. Would Xara give the Chinese shipper more orders if it reduced its shipping costs to $2,500per shipment?ii. Would Xara give the Chinese shipper more orders if it reduced its damaged orders to 5%?iii. Would Xara give the shipper more of its orders if it reduced its travel time to 28 days?