Two advertising media are being considered for promotion of a product. Radio ads
ID: 3157115 • Letter: T
Question
Two advertising media are being considered for promotion of a product. Radio ads cost $400 each, while newspaper ads cost $600 each. The total budget is $7,200 per week. The total number of ads should be at least 15, with at least 2 of each type, and there should be no more than 19 ads in total. The company does not want the number of newspaper ads to exceed the number of radio ads by more than 25 percent. Each newspaper ad reaches 6,000 people, 50 percent of whom will respond; while each radio ad reaches 2,000 people, 20 percent of whom will respond. The company wishes to reach as many respondents as possible while meeting all the constraints stated. If this is formulated as a LP model, with R = number of radio ads placed and N = number of newspaper ads placed, the correct set of constraints would be:
R+N >= 15; R+N <= 19; 400R+600N <= 7200; 1.25R – N <= 7200; R >=2; N >=2
R+N >= 15; R+N <= 19; 400R+600N <= 7200; 1.25R – N <= 7200; R >=2; N >=2; R, N >= 0
R+N >= 15; R+N <= 19; 400R+600N <= 7200; 1.25R + N <= 7200; R >=2; N >=2; R, N >= 0
R+N <= 15; R+N <= 19; 400R+600N <= 7200; 1.25R – N <= 7200; R >=2; N >=2; R, N >= 0
A small furniture manufacturer produces tables and chairs. Each product must go through three stages of the manufacturing process: assembly, finishing, and inspection. Each table requires 3 hours of assembly, 2 hours of finishing, and 1 hour of inspection. Each chair requires 2 hours of assembly, 2 hours of finishing, and 1 hour of inspection. The profit per table is $120 while the profit per chair is $80. Currently, each week there are 200 hours of assembly time available, 180 hours of finishing time, and 40 hours of inspection time. Linear programming is to be used to develop a production schedule. Define the variables as follows:
T = number of tables produced each week
C = number of chairs produced each week
Suppose it is decided that there must be 4 chairs produced for every table. How would this constraint be written?
T C
T C
4T = C
Capital Budgeting Inc has to select among six possible projects without exceeding its total investment budget of $10,000. It’s objective is to maximize the NPV (Net Present Value) of all future earnings form the projects it selects to invest in. The information on the six possible projects for investment is as follows:
Project
Net Present Value (NPV) Of Future Earnings
Investment Required
1
$22,500
$7,500
2
$24,000
$7,500
3
$8,000
$3,000
4
$9,500
$3,500
5
$11,500
$4,000
6
$9,750
$3,500
Use the information above to answer questions 24 - 27
Assuming that Capital Budgeting Inc is allowed to invest partially in any of the projects with expectation that the NPV will be reduced proportionally, the optimal investment would be:
$1500 in Project 3 and $2,500 in Project 2
$2500 in Project 1 and $7,500 in Project 2
$2000 in Project 6 and $7,500 in Project 2
$2000 in Project 1 and $7,500 in Project 2
$2500 in Project 1 and $7,500 in Project 2
Assuming that Capital Budgeting Inc is allowed to invest partially in any of the projects with expectation that the NPV will be reduced proportionally, the max NPV it can earn when it selects its projects optimally is equal to
None of the alternatives are correct.
$27,250
$31, 500
$35,000
$27,550
Ivana Myrocle wishes to invest her inheritance of $200,000 so that her return on investment is maximized, but she also wishes to keep her risk level relatively low. She has decided to invest her money in any of three possible ways: CDs, which pay a guaranteed 6 percent; stocks, which have an expected return of 13 percent; and a money market mutual fund, which is expected to return 8 percent. She has decided that any or all of the $200,000 may be invested, but any part (or all) of it may be put in any of the 3 alternatives. Thus, she may have some money invested in all three alternatives. In formulating this as a linear programming problem, define the variables as follows:
C = dollars invested in CDs
S = dollars invested in stocks
M = dollars invested in the money market mutual fund
Suppose that Ivana has decided that the amount invested in stocks cannot exceed one-fourth of the total amount invested. Which is the best way to write this constraint?
S (C + M) / 4
-C + 3S - M 0
0.13S 0.24C + 0.32M
-C + 4S - M 0
S 100,000/4
Project
Net Present Value (NPV) Of Future Earnings
Investment Required
1
$22,500
$7,500
2
$24,000
$7,500
3
$8,000
$3,000
4
$9,500
$3,500
5
$11,500
$4,000
6
$9,750
$3,500
Explanation / Answer
Radio Newspaper Min/Max Cost 400 600 7200 Max Min 1 1 15 Min Max 1 1 19 Max At least 2R 1 1 Min At least 2N 1 2 Min
N ‰¤ 1.25R Objective: 20 (2000) 5 (6000)
R = # Radio ads N = # Newspaper ads
Therefore A= .20(2000) R + .5(6000) N
Constraints 400 R + 600N ‰¤ 7200 R + N ‰¥ 15 R + N ‰¤ 19 R ‰¥ 2 N ‰¥ 2 R, N ‰¥ 0 1.25 R €“ N ‰¥ 0
2)
400R+ 600N ‰¤ 7200 (4R + 6N ‰¤ 72) R= (0, 18) N= (12, 0)
R + N ‰¥ 15 R= (0, 15) N= (15, 0)
R + N ‰¤ 19 R= (0, 19) N= (19, 0)
R ‰¥ 2 Vertical line
N ‰¥ 2 Horizontal line
1.25 R €“ N ‰¥ 0 R= (0, 10) N= (0, 12.5)
[pic]
3)
Corner Point 1: R+N = 15 4R+6N = 72 Therefore C (9,6) = 21,600
Corner Point 2: N = 2 4R+6N = 72 Therefore C (15,2) = 12,000
Corner Point 3: R = 2 R+N =15 Therefore C (13,2) = 11,200
Conclusion: The corner point 1 with the value of 21,600; is the value at which the objective function is at a maximum