4: a) The map coordinates (shown in parenthesis) of six cities are A(4,7). B(5,10). C(1.9). D(83). E(63) and F9.2). The demand at each city is expected to be 10, 14,5.8. 17 and 9 tons respectively. Near which city should we build a central hub? b) The fixed costs for operating our plant a locations A, B and C, D are $1600, 82300, $2,500, and $4,000 per day respectively. The variable costs are $11,54,57 and $3 per unit respectively. Find the range of production levd where each location is optimal. c) We are trying to lease a warehouse for the next four years. Option 1 is to pay a non-refundable deposit of $20,000 now and then $3,000 per month at the end of each month for the next four years. Another option is to pay one month rent of $3,500 at the beginning of each month for the next four years and a security deposit of $3,500 now which will be returned at the end of the lease period. Find the present value of each option using an interest rate of 7% per year. 4: a) The map coordinates (shown in parenthesis) of six cities are A(4,7). B(5,10). C(1.9). D(83). E(63) and F9.2). The demand at each city is expected to be 10, 14,5.8. 17 and 9 tons respectively. Near which city should we build a central hub? b) The fixed costs for operating our plant a locations A, B and C, D are $1600, 82300, $2,500, and $4,000 per day respectively. The variable costs are $11,54,57 and $3 per unit respectively. Find the range of production levd where each location is optimal. c) We are trying to lease a warehouse for the next four years. Option 1 is to pay a non-refundable deposit of $20,000 now and then $3,000 per month at the end of each month for the next four years. Another option is to pay one month rent of $3,500 at the beginning of each month for the next four years and a security deposit of $3,500 now which will be returned at the end of the lease period. Find the present value of each option using an interest rate of 7% per year