The Shop at Home Network sells various household goods during live television broadcasts. The company owns several warehouses to hold many of the goods it sells but also leases extra warehouse space when needed. During the next five months, the company expects it will need to lease the following amounts of extra warehouse space: Month 1 2 3 4 5 Square Feet Needed 20,000 30,000 40,000 35,000 50,000 At the beginning of any month, the company can lease extra space for one or more months at the following costs: Lease term (months) 1 2 3 4 5 Cost per Sq. Ft. Leased $55 $95 $130 $155 $185 So, for instance, at the start of month 1 the company can lease as much space as it wants for four months at a cost of $155 per square foot. Similarly, at the start of month 3, the company can lease any amount of space for two months at a cost of $95 per square foot. The company wants to determine the least costly way of meeting its warehousing needs over the coming five months. Formulate an LP model for this problem. Create a spreadsheet model for this problem and solve it using Solver. What is the optimal solution? How much would it cost the company to meet its space needs if in each month it leases for one month exactly the amount of space required for the month?
The Shop at Home Network sells various household goods during live television broadcasts. The company owns several warehouses to hold many of the goods it sells but also leases extra warehouse space when needed. During the next five months, the company expects it will need to lease the following amounts of extra warehouse space:
|
Month |
1 |
2 |
3 |
4 |
5 |
|
Square Feet Needed |
20,000 |
30,000 |
40,000 |
35,000 |
50,000 |
At the beginning of any month, the company can lease extra space for one or more months at the following costs:
|
Lease term (months) |
1 |
2 |
3 |
4 |
5 |
|
Cost per Sq. Ft. Leased |
$55 |
$95 |
$130 |
$155 |
$185 |
So, for instance, at the start of month 1 the company can lease as much space as it wants for four months at a cost of $155 per square foot. Similarly, at the start of month 3, the company can lease any amount of space for two months at a cost of $95 per square foot. The company wants to determine the least costly way of meeting its warehousing needs over the coming five months.
- Formulate an LP model for this problem.
- Create a spreadsheet model for this problem and solve it using Solver.
- What is the optimal solution?
- How much would it cost the company to meet its space needs if in each month it leases for one month exactly the amount of space required for the month?
Since you have posted a question with multiple sub-
Linear programming, often known as linear optimization, is a method of obtaining the best feasible solution to a mathematical model by taking into account specific linear connections. It encompasses issues like as maximising revenues, decreasing expenditures, and making the most efficient use of resources, among others. The methods for solving LPP are the Simplex approach or the graphical method.
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