John’s car has an average of 40 miles per gallon (mpg) when using gas from allen’s station and an average of 50 mpg when using gas from bob’s station. john’s preferences are such that he only wants to drive as far as possible given his budget. the gas price is pa dollars at allen’s station and pb dollars at bob’s station. john has a total income of i. write down a utility function u(a, b) that represents john's preferences for gal lons of gas consumed at allen's station, a, and gallons of gas consumed at bob's station b. (hint: treat a and b as two standard consumption goods and find the utility that describes john's preferences for those goods.)

When interest is compounded continuously, the amount of money increases at a rate proportional to the amount s present at time t, that is, ds/dt = rs, where r is the annual rate of interest. (a) find the amount of money accrued at the end of 3 years when $4000 is deposited in a savings account drawing 5 3 4 % annual interest compounded continuously. (round your answer to the nearest cent.) $ (b) in how many years will the initial sum deposited have doubled? (round your answer to the nearest year.) years (c) use a calculator to compare the amount obtained in part (a) with the amount s = 4000 1 + 1 4 (0.0575) 3(4) that is accrued when interest is compounded quarterly. (round your answer to the nearest cent.) s = $

United continental holdings, inc., (ual), operates passenger service throughout the world. the following data (in millions) were adapted from a recent financial statement of united. sales (revenue) $38,901 average property, plant, and equipment 17,219 average intangible assets 8,883 1. compute the asset turnover. round your answer to two decimal places.

Assume a competitive firm faces a market price of $60, a cost curve of c = 0.003q^3 + 25q + 750, and a marginal cost of curve of: mc = 0.009q^2 + 25.the firm's profit maximizing output level (to the nearest tenth) is , and the profit (to the nearest penny) at this output level is $ will cause the market supply to (shift right/shift left). this will continue until the price is equal to the minimum average cost of $