1. (50 points) Amazon needs to lease warehouse storage space over the next five months to be able to fulfill its 2-day delivery promise to a region with seasonal demand. The data on required space in each month; and different lease periods and their associated costs are given below. Note that the space requirements are quite different in each month and longer lease terms have lower cost per month. Month 1 2 3 4 5 Required Space (in 1000 sq. ft.) 30 20 40 10 50 Leasing period 1-month 2-month 3-month 4-month 5-month Cost per 1000 sq. ft. leased 65,000 100,000 135,000 160,000 190,000 For example, a feasible lease plan is to sign a 3-month lease in the first month for 30,000 sq. ft. at a cost of 30 x $135,000 = $4,050,000. At the beginning of the third month, Amazon still has one month left on the previous lease. So it can sign an additional 2-month lease for 10,000 sq. ft. at a cost of 10 x $100,000 = $1,000,000, to cover the additional requirement of 10,000 sq. ft. Finally, at the beginning of month 5, the previous leases expire, so Amazon can sign a one-month lease of 50,000 sq. ft. at a cost of 50 x $65,000 = $3,250,000. The overall cost of this lease plan is $8,300,000 and it meets the minimum space requirements in each month. Alternatively, at the beginning of the first month, the company can sign a 5-month lease of 50,000 sq. ft. (this is the maximum space needed) at a total cost of $9,500,000. Clearly, the former lease plan is much cheaper. (a) (35 points) Formulate a linear program to determine a lease plan so that the total cost of leasing is minimized. Clearly describe your decision variables, objective function and con- straints. (b) (15 points) Solve this problem in AMPL. Include screenshots as part of your main answer file. The AMPL files should be uploaded in one zipped folder as a supplement. 1. (50 points) Amazon needs to lease warehouse storage space over the next five months to be able to fulfill its 2-day delivery promise to a region with seasonal demand. The data on required space in each month; and different lease periods and their associated costs are given below. Note that the space requirements are quite different in each month and longer lease terms have lower cost per month. Month 1 2 3 4 5 Required Space (in 1000 sq. ft.) 30 20 40 10 50 Leasing period 1-month 2-month 3-month 4-month 5-month Cost per 1000 sq. ft. leased 65,000 100,000 135,000 160,000 190,000 For example, a feasible lease plan is to sign a 3-month lease in the first month for 30,000 sq. ft. at a cost of 30 x $135,000 = $4,050,000. At the beginning of the third month, Amazon still has one month left on the previous lease. So it can sign an additional 2-month lease for 10,000 sq. ft. at a cost of 10 x $100,000 = $1,000,000, to cover the additional requirement of 10,000 sq. ft. Finally, at the beginning of month 5, the previous leases expire, so Amazon can sign a one-month lease of 50,000 sq. ft. at a cost of 50 x $65,000 = $3,250,000. The overall cost of this lease plan is $8,300,000 and it meets the minimum space requirements in each month. Alternatively, at the beginning of the first month, the company can sign a 5-month lease of 50,000 sq. ft. (this is the maximum space needed) at a total cost of $9,500,000. Clearly, the former lease plan is much cheaper. (a) (35 points) Formulate a linear program to determine a lease plan so that the total cost of leasing is minimized. Clearly describe your decision variables, objective function and con- straints. (b) (15 points) Solve this problem in AMPL. Include screenshots as part of your main answer file. The AMPL files should be uploaded in one zipped folder as a supplement