A foreign-car dealer with warehouses in Omaha and Detroit receives orders from dealers in Chicago and New York. The dealer in Chicago needs 65 cars and the dealer in New York needs 80. The Omaha warehouse has 110 cars and the Detroit warehouse has 125. The cost of shipping cars from Detroit to Chicago is $140 per car, from Detroit to New York $230 per car, from Omaha to Chicago $110 per car, and from Omaha to New York $150 per car.

Use Linear Programming, in 2 Variables only, and graphing method to find the number of cars to be shipped from each warehouse to each dealer to minimize the shipping cost. Let x = number of cars shipped from Detroit to New York, and y = number of cars shipped from Detroit to Chicago .

1. Organize the information in a schematic diagram. Fully label your diagram
2. Formulate a complete linear programming problem
3. Sketch the feasible set. Show all the details. Fully label your graph. Cross out the half-plane that does not fulfill each inequality. Find all the vertices of the feasible set.
4. Use the Fundamental Theorem of Linear Programming to determine the optimal point.