1. The following table gives the map coordinates and the shipping loads for a set of cities that we wish to connect through a central hub.
|
City
|
Map coordinates (x, y)
|
Shipping load (in tons)
|
|
A
|
(50, 10)
|
20
|
|
B
|
(20, 5)
|
10
|
|
C
|
(15, 10)
|
30
|
|
D
|
(20, 5)
|
20
|
Using the Centroid method, at what map coordinates should the central hub be located? Please provide at least one step of calculation for each of the two coordinates of the centroid for full credit.
2. A company plans to build a new production facility and has two locations to choose from. A new facility at location A will incur a total fixed cost of $1 million a year and a per-unit variable cost of $4. At location B, a total fixed cost of $2 million will be incurred, together with a per-unit variable cost of $3.
(a) What is the break-even point? Please provide the formula, at least one step of calculation, and the correct answer for full credit.
(b) If the expected production volume is 1 million units, which location gives a lower total cost? Please provide at least one step of calculation and the correct answer for full credit.
3. Ray's Satellite Emporium wishes to determine the best order size for its best-selling satellite dish. The annual demand of the model is 10,000 units. The inventory holding cost of the model is 20% of the wholesale price. It costs $50 to place an order with the supplier of the satellite dish.
Suppose the wholesale price of the satellite dish is $100 per unit. How many units should Ray order each time using the EOQ model? Please provide the formula, at least one step of calculation, and the correct order size for full credit.