Quantitative Methods for Businesses

 

1. An investment firm has $1 million to invest in stocks, bonds, certificates of deposit, and real estate. The firm wishes to determine the mix of investments that will maximize the cash value at the end of 6 years.
Opportunities to invest in stocks and bonds will be available at the beginning of each of the next 6 years. Each dollar invested in stocks will return $1.20 (a profit of $0.20) 2 years later; the return can be immediately reinvested in any alternative. Each dollar invested in bonds will return $1.40 3 years later; the return can be reinvested immediately.
Opportunities to invest in certificates of deposit will be available only once, at the beginning of the second year. Each dollar invested in certificates will return $1.80 four years later. Opportunities to invest in real estate will be available at the beginning of the fifth and sixth years. Each dollar invested will return $1.10 one year later.
To minimize risk, the firm has decided to diversify its investments. The total amount invested in stocks cannot exceed 30% of total investments, and at least 25% of total investments must be in certificates of deposit.
The firm’s management wishes to determine the optimal mix of investments in the various alternatives that will maximize the amount of cash at the end of the sixth year.
a. Formulate a linear programming model for this problem.
b. Solve the model by using the computer.

2. The manager of a department store in Seattle is attempting to decide on the types and amounts of advertising the store should use. He has invited representatives from the local radio station, television station, and newspaper to make presentations in which they describe their audiences.
The television station representative indicates that a TV commercial, which costs $15,000, would reach 25,000 potential customers. The breakdown of the audience is as follows:

Male Female
Senior 5,000 5,000
Young 5,000 10,000

The newspaper representative claims to be able to provide an audience of 10,000 potential customers at a cost of $4,000 per ad. The breakdown of the audience is as follows:

Male Female
Senior 4,000 3,000
Young 2,000 1,000

The radio station representative says that the audience for one of the station’s commercials, which costs $6,000, is 15,000 customers. The breakdown of the audience is as follows:

Male Female
Senior 1,500 1,500
Young 4,500 7,500
The store has the following advertising policy:
• Use at least twice as many radio commercials as newspaper ads.
• Reach at least 100,000 customers.
• Reach at least twice as many young people as senior citizens.
• Make sure that at least 30% of the audience is female.

Available space limits the number of newspaper ads to seven. The store wants to know the optimal number of each type of advertising to purchase to minimize total cost.
a. Formulate a linear programming model for this problem.
b. Solve the model by using the computer.
c. Suppose a second radio station approaches the department store and indicates that its commercials, which cost $7,500, reach 18,000 customers with the following demographic breakdown:

Male Female
Senior 2,400 3,600
Young 4,000 8,000

If the store considered this station along with the other media alternatives, how would this affect the solution?
Hint: we have 4 variables only

 

 

 

 

 

Sample Solution

Is Hillary Clinton Electable? GuidesorSubmit my paper for examination Hillary Rodham Clinton may turn into the principal female President of the United States of America—some time ago being the First Lady, a representative, and the Secretary of State—as she is running as an applicant in the 2016 presidential political race. It is significant, in this manner, to decide whether she is a degenerate lawmaker and should hold office as the President of the USA. From her various outrages, her acknowledgment of battle cash from lobbyists and organizations, and her misleading the overall population all the time, I trust Hillary Rodham Clinton ought not be chosen as President of the USA. On the off chance that one kinds “Hillary Clinton embarrassments” in any web crawler on the Internet, one will perpetually discover endless articles on her times of outrages even ones that are going on now, for example, the FBI test into her private email server as Secretary of State and her Clinton Foundation misdealings with accounts (McLendon, Inquistr). Despite the fact that Clinton is yet to be accused of a criminal offense, her incalculable embarrassments don’t show her in a decent light–particularly when she is a legal counselor and realizes how to evade the legal framework (Calabrese, Eohistory). The absolute most celebrated outrages she has been engaged with are: misusing the assault on the US office in Benghazi in 2011; the way that she gets paid $275,000 by and large for every open discourse; the Whitewater embarrassment, which began as a property undertaking and wound up as illicit advances, tax avoidance, and even a potential demise; and Filegate, which emerged in 1996, was an ill-advised access to FBI records that was arranged by Hillary Clinton (Gobry, The Week). Notwithstanding, Clinton has not been charged or captured for any of these outrages, considerably following quite a while of being confronted with claims. However, not being demonstrated blameworthy in court is definitely not a last sign of being guiltless (particularly with prominent individuals with enormous cash, for example, the OJ Simpson case, where the jury succumbed to the barrier’s stunts and didn’t follow the profoundly point by point DNA proof that was given (Quora). Be that as it may, if these outrages are insufficient to make you discouraged in deciding in favor of her, you should focus on the cash she takes from lobbyists and organizations to work for their exceptional advantages. Majority rules system Now! reports that, “As indicated by another report by Greenpeace, Hillary Clinton’s presidential crusade and the super PAC supporting her have gotten $138,400 from non-renewable energy source lobbyists and $1,327,210 from bundlers, totaling more than $4.5 million from lobbyists, bundlers and enormous givers associated the non-renewable energy source industry” (Cray, Democracy Now!). This is a clashing message that Mrs. Clinton is giving when she says she needs to work for environmental change (Hillary Clinton Campaign, Hillary Clinton). Also, she has gotten a large number of dollars from different huge enterprises, with the top organization, Soros Fund Management, giving her $7,039,900 (Open Secrets). On the off chance that she is taking this a lot of cash from lobbyists and enterprises, in what manner can an American resident trust she will work for the normal individual, rather than her rich and politicized contributors? Then again, however, the Clinton Foundation, which Hillary Clinton is effectively associated with, offers plentifully to mankind. “On account of our work, in excess of 31,000 American schools are furnishing kids with sound nourishment decisions with an end goal to destroy youth heftiness; in excess of 105,000 ranchers in Malawi, Rwanda, and Tanzania are profiting by atmosphere shrewd agronomic preparing, more significant returns, and expanded market get to; in excess of 33,500 tons of ozone harming substance emanations are being decreased yearly over the United States… ” (Clinton Foundation). Nonetheless, this equivalent Clinton Foundation has been blamed for misrepresentation and is as of now under tension by the US Congress to find a workable pace of their deceptive with outside countries in respect for pay-for-play ventures (Investor’s Business Daily). It very well may be said that Mrs. Clinton is an obsessive liar. She lied about being under expert marksman fire in Bosnia in 1996. Likewise, as indicated by American Thinker, “Mrs. Clinton lied about a video causing the Benghazi fear assault and is presently multiplying down, denying she deceived the exploited people’s families about the video, accusing her manufacture for the “mist of war. There’s is additionally her messages, which she lied going to Congress and the American individuals. These aren’t the unimportant manufactures about whom she was named after, however genuine bogus proclamations including loss of American life and traded off U.S. international strategy and national security” (Joondeph, American Thinker). Lying is certainly not an uncommon thing for Mrs. Clinton. William Safire of the NY Times wrote in 1996 that Hillary “is an innate liar.” He examined her trickery starting in Arkansas and all path to the White House: Travelgate, Whitewater, missing charging records, and lost FBI documents, to make reference to a couple of smoke screens (Joondeph, American Thinker). Indeed, even during the 1970s, Mrs. Clinton was terminated from her situation on the Watergate House Judiciary Committee over “lies and untrustworthy conduct” (Calabrese, Eohistory). Somebody who has a reputation of lying about such critical and touchy data ought not be chosen president. Another approach to see her lying is that by PolitiFact’s numbers, her lying is somewhat less than most government officials (PolitiFact). In any case, that isn’t motivation to expel her falsehoods, as lying in any example, particularly as a local official, isn’t dependable or reliable. And furthermore, Politifact and other mainstream sites for indicating realities have been found to have inclination (politifactbias). Despite the fact that Hillary Rodham Clinton is a commonly recognized name, her positivity evaluations are lower than any time in recent memory. Despite the fact that she has been the First Lady, the Secretary of State, and a New York state congressperson, this doesn’t mean she is electable. Indeed, she has had a series of outrages ascribed to her all through her political profession, she acknowledges gigantic totals of cash from lobbyists and enterprises, and she has lied on record to the American open and the US government on many occasions. Despite the fact that she may been winning the popularity based essential political decision right now, we can’t neglect her degenerate and pretentious conduct, particularly when she is as a rule at present researched by the FBI for her misusing of ordered data on her private email servers and for her Clinton Foundation money related misdealings. References Mclendon, Kim. “Hillary Clinton is Under Investigation by the FBI for More than E-Mail: If Elected, Could She Be Impeached?” The Inquisitr News. N.p., 17 May 2016. Web. 17 May 2016. Calabrese, Dan. “Hillary Rodham Clinton History.” Hillary Rodham Clinton History. N.p., n.d. Web. 17 May 2016. Gobry, Pascal-Emmanuel. “Hillary Clinton’s Litany of Scandal.” Hillary Clinton’s Litany of Scandal. N.p., 31 Mar. 2016. Web. 17 May 2016. Cray, Charlie. “The amount Money has Hillary Clinton’s Campaign Taken from Fossil Fuel Companies?” Democracy Now! N.p., n.d. Web. 17 May 2016. “Hillary Clinton’s Plan to Take on Climate Change.” Taking on the Global Threat of Climate Change. N.p., n.d. Web. 17 May 2016. “Hillary Clinton (D).” Opensecrets RSS. N.p., n.d. Web. 17 May 2016. Joondeph, Brain. “Blog: Is Hillary Clinton a Compulsive Liar?” Blog: Is Hillary Clinton a Compulsive Liar? N.p., n.d. Web. 17 May 2016. “For what reason was OJ Simpson Acquitted? What Factors Went into the Juror’s Decision? How Did the Prosecution Lose the Case?” – Quora. N.p., n.d. Web. 02 Aug. 2016. “About Us.” Clinton Foundation. N.p., n.d. Web. 02 Aug. 2016. EDIT2. “Outrage Without End: Is The Clinton Foundation A Fraud?” Investor’s Business

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