The Shop at Home Network sells various household goods during live television broadcasts. The company owns...

 

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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 sqft Needed 1 20,000 2 30,000 3 4 5 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 1 2 3 4 5 (months) Cost per sqft $55 $95 $130 $175 $185 So, for instance, at the start of month 1 the company can lease as much space it wants for four months at a cost of $175 per sqft. Similarly, at the start of month 3, the company can lease any amount of space for two months at a cost of $95 per sqft. The company wants to determine the least costly way of meeting its warehousing needs over the coming five months. a. Formulate an LP model for this problem. (20 points) b. Create a spreadsheet model for this problem and solve it using Solver. (40 points) c. What is the optimal solution? (20 points) d. 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? (20 points) Leased in month 1 2 3 4 5 1 2 Shop @ Home Through month 3 4. 5 Leasing costs $55 $95 $130 $175 $185 $55 $95 $130 $175 $55 $95 $130 $55 $95 $55 Total leasing cost Total Total Available Needed 20000 30000 40000 35000 50000 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 sqft Needed 1 20,000 2 30,000 3 4 5 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 1 2 3 4 5 (months) Cost per sqft $55 $95 $130 $175 $185 So, for instance, at the start of month 1 the company can lease as much space it wants for four months at a cost of $175 per sqft. Similarly, at the start of month 3, the company can lease any amount of space for two months at a cost of $95 per sqft. The company wants to determine the least costly way of meeting its warehousing needs over the coming five months. a. Formulate an LP model for this problem. (20 points) b. Create a spreadsheet model for this problem and solve it using Solver. (40 points) c. What is the optimal solution? (20 points) d. 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? (20 points) Leased in month 1 2 3 4 5 1 2 Shop @ Home Through month 3 4. 5 Leasing costs $55 $95 $130 $175 $185 $55 $95 $130 $175 $55 $95 $130 $55 $95 $55 Total leasing cost Total Total Available Needed 20000 30000 40000 35000 50000