Everest sells many different products online. Everest owns several distribution centers where it stores many of its product lines, but it also leases extra space from a third$-$party provider when necessary. During the next $5$ months, Everest predicts it will need to lease the following amounts of extra storage space:

Month $12345$

Square Meters Needed $1,8582,7872,3233,2523,252$

At the beginning of any month, Everest can lease extra space for one or more months at the following costs:

Lease Term $($Months$)12345$

Cost per square meter leased $$600$ $$1,025$ $$1,400$ $$1,670$ $$2,045$

For example, at the beginning of month $1,$ Everest can lease as much space as it wants for $3$ months at a cost of $$1,400$ per square meter. Similarly, at the start of month $2,$ it can lease any amount of space for $1$ month at a cost of $$600$ per square meter. Everest wants to determine the most inexpensive way of meeting its storage needs over the coming $5$ months.

Develop and solve an optimization model to accomplish this task. $($For the decision variables, let xij be the number of square feet to lease in month i for j months. This has already been laid out for you in the worksheet.$)$ Also, answer the following questions in the highlighted cells N$2$:N$8.$

What is the minimum cost required to satisfy Everest's storage needs?

In the optimal solution, how many square meters should they lease in Month $2$ for four months?

How much would it cost Everest to meet its storage needs if in each month, it leases for $1$ month exactly the amount of space required for the month?

By how much would the minimum cost increase if Everest needed an additional square meter of storage in Month $3?$

Which value should be used to answer question d$?($Select the best answer.$)$

By how much would the cost per square meter for a three$-$month lease have to decrease in order for Everest to lease any space for three months in Month $2?$

Which value should be used to answer question f$?($Select the best answer.$)$

Everest sells many different products online. Everest owns several distribution centers where it stores many of its product lGalapagos sells many different products online. Galapagos owns several distribution centers where it stores many of its product lines, but it also leases extra

space from a third$-$party provider when necessary. During the next $5$ months, Galapagos predicts it will need to lease the following amounts of extra storage

space:

At the beginning of any month, Galapagos can lease extra space for one or more months at the following costs:

For example, at the beginning of month $1,$ Galapagos can lease as much space as it wants for $3$ months at a cost of $$1,400$ per square meter. Similarly, at the start

of month $2,$ it can lease any amount of space for $1$ month at a cost of $$600$ per square meter. Galapagos wants to determine the most inexpensive way of meeting

its storage needs over the coming $5$ months.

Develop and solve an optimization model to accomplish this task. $($For the decision variables, let xij be the number of square meters to lease in month i for $j$

months. This has already been laid out for you below.$)$ Also, answer the following questions in the highlighted cells N$2$:N$8.$

a$)$ What is the minimum cost required to satisfy Galapagos's storage needs?

b$)$ In the optimal solution, how many square meters should they lease in Month $2$ for four months?

c$)$ How much would it cost Galapagos to meet its storage needs if in each month, it leases for $1$ month exactly the amount of space required for the month?

d$)$ By how much would the minimum cost increase if Galapagos needed an additional square meter of storage in Month $3?$

e$)$ Which value should be used to answer question d$?($Select the best answer.$)$

f$)$ By how much would the cost per square meter for a three$-$month lease have to decrease in order for Galapagos to lease any space for three months in Month $2?$

g$)$ Which value should be used to answer question f$?($Select the best answer.$)$

Square meters leased