a) (5 points): The map coordinates (shown in parenthesis) of six cities are A(4,7), B(5,10), C(7,9), D(8,3), E(6,3), and F(9,2). The demand at each city is expected to be 20, 15, 12, 10, 8, and 15 tons respectively. Find the hub coordinates and the total ton-miles driven. Near which city should we build a central hub?

b) (5 points): The fixed costs for operating our plant at locations A, B, and C, D are $1300, $1000, $2,200, and $4,000 per day respectively. The variable costs are $7, $11, $4and $2 per unit respectively. Find the range of production level where each location is optimal. `

c) (5 points): We are trying to lease a warehouse for the next four years. Option 1 is to pay a non-refundable deposit of $30,000 now and then $4,200 per month at the end of each month for the next four years. Another option is to pay one month rent of $4,700 at the beginning of each month for the next four years and a security deposit of $4,700 now which will be returned at the end of the lease period. Find the present value of each option using an interest rate of 8% per year.

SOLVE ONLY C