Question 1:
A company is trying to determine how to allocate its $145,000 advertising budget for a new product. The company is considering newspaper ads and television commercials as its primary means for advertising. The following table summarizes the costs of advertising in these different media and the number of new customers reached by increasing amounts of advertising.
Media and # of Ads # New Customers Reached Cost per Ad
Newspaper: 1-10 900 $1,000
Newspaper: 11-20 700 $900
Newspaper: 21-30 400 $800
TV: 1-5 10,000 $12,000
TV: 6-10 7,500 $10,000
TV: 11-15 5,000 $8,000
For instance, each of the first 10 ads the company places in newspapers will cost $1,000 and is expected to reach 900 new customers. Each of the next 10 newspaper ads will cost $900 and is expected to 700 new customers. Note that the number of new customers reached by increasing amounts of advertising decreases as the advertising saturates the market. Assume the company will purchase no more than 300 newspaper ads and no more than 15 television ads.
a) Formulate an LP model for this problem to maximize the number of new customers reached by advertising.
b) Implement your model in AMPL and in a spreadsheet and solve it.
c) What is the optimal solution?
d) Suppose the number of new customers reached by 11-20 newspaper ads is 400 and the number of new customers reached by 21-30 newspaper ads is 700. Make those changes in your spreadsheet and reoptimize the problem. What is the news optimal solution? What (if anything) is wrong with this solution and why?
Question 2 :
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/Square Foot 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.
a) Formulate an LP model for this problem.
b) Create a spreadsheet model for this problem, and solve it using Solver. Also solve it using AMPL.
c) What is the optimal solution?
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?
REQUIREMENTS:
1. Please attach Excel spreadsheet with answers that solved by excel.
2. For AMPL question please attach Notepad documents.