If x 1 and x 2 are the number of items of two goods bought, a customer’s utility is U ( x 1 , x 2 ) = 2 x 1 x 2 + 3 x 1 . The unit cost is $ 1 for the first good and $ 3 for the second. Use Lagrange multipliers to find the maximum value of U if the consumer’s disposable income is $ 100 . Estimate the change in optimal utility if the consumer's disposable income increases by $ 8 .

An epedemic is spreading form human to human. A hospital counts on the start of the epidemic 100 infected patients visiting on one day. One day later the number of patients coming is 300. Calculate the time constant of the spreading of the disease and calculate when the first infected entered the population. We estimate that the epidemic is controllable by a medicine, a single dose. How many doses do we need if the epidemic is spreading for 14 days?

Assume you just graduated from a university with an MBA and were hired by a small American company generating 100% of its $20 million revenue from domestic sales. Your job as International Sales Director is quite simple: to make sure international sales generate as much revenue as domestic sales within five years.

Where do you start?

What are some of your first initiatives? Why?

The following frequency table summarizes the distances in miles of 100 patients from a regional hospital.

Distance Frequency

0-4 20

4-8 25

4-12 30

12-16 20

16-24 5

Calculate the sample variance and standard deviation for this data (since it is a case of grouped data- use group or class midpoints in the formula in place of X values, and first calculate the sample mean)

(Mobile generations & 5G mobile) Mobile communications have been developed from the first generation (1G) to the fifth generation (5G) now. Explain each mobile generation from 1G to 5G in brief. Describe the differences of each generation from the previous generation. Discuss what 5G mobile is different from the previous generations of mobile. Show your idea how to utilize the 5G mobile for business. (100 points)

The unpaid balance at the start of a 28-day billing cycle was $990.01. A $6,000 purchase was made on the first day of the billing cycle and a $100 payment was credited to the account on day 21. How much interest will be charged at the end of the billing cycle? Assume that the annual interest rate on a credit card is 24.07% and interest is calculated by the average daily balance method.

At the end of the billing cycle, $_______ will be charged in interest.

(Round to the nearest cent as needed)

1.During an extraction, a solute (S) will partition itself between two immiscible solvents phases [S (solvent 1)   S (solvent 2)] with a partition coefficient defined as If solute X is 1.5 times more soluble in solvent 2 than it is in solvent 1 it has a partition coefficient of 1.5. Suppose a reaction mixture, when diluted with water, afforded 300 mL of an aqueous solution of 30 g of the reaction product malononitrile [CH₂(CN)₂], which is to be isolated by extraction with ether. The solubility of malononitrile in ether at room temperature is 20.0 g/100 mL, and in water is 13.3 g/100mL. The ratio of these quantities is equal to the partition coefficient, k, which equals

What percent of malononitrile would be recovered by extraction of (a) three successive 100-mL portions of ether and (b) one 300-mL portion of ether? SHOW WORK (Can be written in pen and attached to report). Suggestion: For each extraction, let x equal the weight extracted into the ether layer. In part (a), for the first of the three extractions, the concentration of malononitrile in the ether layer is x/100 and in the water layer is (30-x)/300. Note in the 2^nd of the 3 100-mL extraction the grams of malononitrile is no longer 30.

8) a. Suppose a 7.6% semi-annual coupon 20-year Treasury issue with a par value of $100 issue is priced in the market based on the on-the-run 20-year Treasury yield. Assume further that this yield is 6.20%, so that each cash flow is discounted at 6.20% divided by 2. What is the market price of the Treasury issue based on this assumption?

b. Suppose also that the price of the same Treasury issue would be $108.462 if it is calculated based on the prevailing Treasury spot rate curve. What action would a dealer take and what would the arbitrage profit be? Can this situation persist in the long run?

The 2020 demand and supply equations for Ontario grapes are as follows:

P = $100 - Q_d^Can                                                          (1)

P = $10 + Q_s^Can                                                         (2)

As a result of a recent visit by Pottsville’s High Commissioner to this week’s virtual Grape and Wine Festival, the Republic of Pottsville has agreed to buy Ontario grapes. Its demand is given as follows:

P = 80-2Q_d^Pottsville                                                                             (10)

                                                What are the economic effects of this new demand?

Original price (1 mark)                    Original output (1 mark)      

New price      ___________ (2 mark)                     New output _____________(2 mark)      

Consumption by Canadians_______ (2 mark)       By Pottsvillians____________(2 mark)