1. Each year, Data Corporal produces up to 5000 computers in Boston and up to 3500 computers in Charlotte. There are customers in Los Angeles, New York, and Seattle who must receive 2300, 3700, and 1300 computers, respectively. Producing a computer costs $250 in Boston and $275 in Charlotte. Computers are transported by plane and can be sent through Chicago. The costs of sending a computer between pairs of cities are shown in the table below.
From Chicago Los Angeles New York Seattle
Boston $40 $80 $30 $75
Charlotte $45 $75 $55 $85
Chicago $65 $45 $60
a. Determine how to minimize the total cost of production and shipping to meet Data Corporal's annual demand. Why doesn't it make sense to ship any computers through Chicago? (Optimal cost - $2,263,500)
b. Modify the model so that no more than 1250 computers can be shipped between any two cities, and find the optimal solution to this modified model. Why are computers now shipped through Chicago?
2. A truck must travel from New York to Los Angeles. As shown in the figure below, several routes are available. The number associated with each arc is the number of gallons of fuel required by the truck to traverse that arc. Determine the route from New York to Los Angeles that uses the minimum amount of gas. (Optimal value - 2450)
3. Allied Freight supplies goods to three customers, who each require 30 units. The company has two warehouses. In warehouse 1, 40 units are available, and in warehouse 2, 30 units are available. The costs of shipping one unit from each warehouse to each customer are shown below. There is a penalty for each unsatisfied customer unit of demand - with customer 1, a penalty cost of $90 is incurred; with customer 2, $80; and with customer 3, $110.
From Customer 1 Customer 2 Customer 3
Warehouse 1 $15 $35 $25
Warehouse 2 $10 $30 $40
Penalty cost $90 $80 $110
a. Determine how to minimize the sum of penalty and shipping costs. Optimal cost - $3,000)
b. Use SolverTable to see how a change in the unit penalty cost of customer 3 ($30 to $130 in steps of $10) affects the optimal cost.
c. Use SolverTable to see how a change in the capacity of warehouse 2 (10 to 70 in steps of 10) affects the optimal cost.
d. Use SolverTable to see what happens to the shipping cost, penalty cost and total cost as all the customer demand simultaneously change by the same percentage. Vary the percentages from -25% to +10% in steps of 5%.