1, You own a hamburger franchise and are planning to shut downoperations for the day, but you are left with 11 buns, 13 defrostedbeef patties, and 10 opened cheese slices. Rather than throw themout, you decide to use them to make burgers that you will sell at adiscount. Plain burgers each require 1 beef patty and 1 bun, doublecheeseburgers each require 2 beef patties, 1 bun, and 2 slices ofcheese, while regular cheeseburgers each require 1 beef patty, 1bun, and 1 slice of cheese. How many of each should you make? HINT[See Example 1.]
plain burgersdouble cheeseburgersregular cheeseburgers
2, Inverse mutual funds, sometimes referred to as "bear market"or "short" funds, seek to deliver the opposite of the performanceof the index or category they track, and can thus be used bytraders to bet against the stock market. This question is based onthe following table, which shows the performance of three suchfunds as of February 27, 2015.
| Year-to-dateLoss |
|---|
| SHPIX (Short Smallcap Profund) | 4% |
|---|
| RYURX (Rydex Inverse S&P 500) | 3% |
|---|
| RYCWX (Rydex Inverse Dow) | 6% |
|---|
You invested a total of $11,000 in the three funds at thebeginning of 2015, including an equal amount in RYURX and RYCWX.Your year-to-date loss from the first two funds amounted to $290.How much did you invest in each of the three funds?
SHPIX$
RYURX$
RYCWX$
At the end of a certain year, the four companies with thelargest number of home Internet users in the United States wereMicrosoft, Time Warner,Yahoo, and Google, with acombined audience of 284 million users. Taking x to be theMicrosoft audience in millions, y the Time Warner audiencein millions, z the Yahoo audience in millions, andu the Google audience in millions, it was observedthat
| | | | | z | ? | u | = | 3(x? y) + 22 |
| | | | | x | + | y | = | 44 +z + u |
| and | x | ? | y | + | z | ? | u | = | 46. |
3, How large was the audience of each of the four companies atthe end of that year?
| Microsoft | million |
| Time Warner | million |
| Yahoo | million |
| Google | million |
4, In the 1990s, significant numbers of tourists traveled fromNorth America and Asia to Australia and South Africa. In 1998, atotal of 2,231,000 of these tourists visited Australia, while388,000 of them visited South Africa. Also, 630,000 of thesetourists came from North America, and a total of 2,619,000 touriststraveled from these two regions to these two destinations. (Assumeno single tourist visited both destinations or traveled from bothNorth America and Asia.)
(a) The given information is not sufficient to determine thenumber of tourists from each region to each destination. Why?
This system has no solution.This system has infinitely manysolutions. This system has finite number ofsolutions.This system has one solution.
(b) If you were given the additional information that a total of1,989,000 tourists came from Asia, would you now be able todetermine the number of tourists from each region to eachdestination?
YesNo
If so, what are these numbers? (If the given information is notsufficient, enter NONE in all answer blanks.)
| from North America to Australia | tourists |
| from North America to South Africa | tourists |
| from Asia to Australia | tourists |
| from Asia to South Africa | tourists |
(c) If you were given the additional information that 199,000tourists visited South Africa from Asia, would you now be able todetermine the number of tourists from each region to eachdestination?
YesNo
If so, what are these numbers? (If the given information is notsufficient, enter NONE in all answer blanks.)
| from North America to Australia | tourists |
| from North America to South Africa | tourists |
| from Asia to Australia | tourists |
| from Asia to South Africa | tourists |
