1. The aggravateseer of Collins Import Autos regards the sum of cars sold in a day (Q) depends on two factors: (1) the sum of hours the dealership is known (H) and (2) the sum of salespersons instituted that day (S). After collecting postulates for two months (53 days), the aggravateseer estimates the subjoined log-rectilinear example:
a. Explain, how to metamorphose the log-rectilinear example into rectirectilinear frame that can be estimated using multiple retrogradation dissection.
The computer output for the multiple retrogradation dissection is shown below:
b. How do you represent coefficients b and c? If the dealership acceptions the sum of salespersons by 20%, what gain be the percentage acception in daily sales?
c. Test the aggravateall example for statistical opinion at the 5% opinion smooth.
d. What percent of the whole departure in daily auto sales is explained by this equation? What could you insinuate to acception this percentage?
e. Test the catch for statistical opinion at the 5% smooth of opinion. If H and S twain similar 0, are sales expected to be 0? Explain why or why not?
f. Test the estimated coefficient b for statistical opinion. If the dealership decreases its hours of exercise by 10%, what is the expected application on daily sales?
2. Using the optimization supposition, dissect the subjoined quotations:
a. The optimal sum of intercourse deaths in the United States is naught.
b. Any taint is too plenteous taint.
c. We cannot drag US troops out of Afghanistan. We entertain committed so plenteous already.
d. If Congress cuts out the Interpolitical Space Station (ISS), we gain entertain ghastly all of the instrument that we entertain already late on it. Therefore, we must hold funding the ISS.
e. Since JetGreen Airways has practiced a 25% acception in its security premiums, the airline should acception the sum of passengers it serves proximate territory in command to divulge the acception in premiums aggravate a larger sum of tickets.
3. You are interviewing three candidates for one sales job posture. On the cause of your experiment and insight, you regard Jane can vend 600 aces a day, Joe can vend 450 aces a day, and Joan can vend 400 aces a day. The daily allowance each individual is question is as follows: Jane $200; Joe $150; and Joan $100. How would you dispose the three applicants?
4. Bavarian Crystal Works designs and fruits control crystal wine decanters for ship-fruit to interpolitical chaffers. The origination aggravateseer of Bavarian Crystal Works estimates whole and ultimate origination requires to be
where requires are measured in U.S. dollars and Q is the sum of wine decanters done year-by-year. Because Bavarian Crystal Works is the simply one of numerous crystal fruitrs in the cosmos-people chaffer, it can vend as numerous of the decanters as it wishes for $70 individually. Whole and ultimate fruits are TR = 70Q and MR = 70 where fruitss are measured in U.S. dollars and Q is the annual decanter origination.
a. What is the optimal smooth of origination of wine decanters? What is the ultimate fruits from the last wine decanter sold?
b. What are the whole fruits, whole require, and net favor (profit) from vending the optimal sum of wine decanters?
c. At the optimal smooth of origination of decanters, an extra decanter can be sold for $70, thereby increasing the whole fruits by $70. Why does the aggravateseer of this secure not fruit and vend one past ace?
5. A judgment manufacturer wishes to maximize whole favor, B = 3x + xy + y topic to the require distraction, C = 4x + 2y = 70. Setup the Lagrangian and then particularize the values of x and y at the incompleteness smooth of favor, ardent the distraction. What are the apex favors?
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