No fly corporation sells three different models of a mosquito "zapper." model a12 sells for $51 and has variable costs of $41. model b22 sells for $109 and has variable costs of $80. model c124 sells for $403 and has variable costs of $321. the sales mix of the three models is a12, 59%; b22, 30%; and c124, 11%. if the company has fixed costs of $174,316, how many units of each model must the company sell in order to break even?

David consumes two things: gasoline (g) and bread (b). david's utility function is u(g, b) = 10g^0.25 b^0.75. use the lagrange technique to solve for david's optimal choices of gasoline and bread as a function of the price of gasoline, p_g, the price of bread, p_b, and his income m. with recent decrease in the price of gasoline (maybe due to external shock such as shale gas production) does david increase his consumption of gasoline? for david, how does partial differential g/partial differential p_g depend on his income m? that is, how does david's change in gasoline consumption due to an increase in the price of gasoline depend on his income level? to answer these questions, find the cross-partial derivative, |partial differential^2 g/partial differential m partial differential p_g.

Financial performance is measured in many ways. requirements 1. explain the difference between lag and lead indicators. 2. the following is a list of financial measures. indicate whether each is a lag or lead indicator: a. income statement shows net income of $100,000 b. listing of next week's orders of $50,000 c. trend showing that average hits on the redesigned website are increasing at 5% per week d. price sheet from vendor reflecting that cost per pound of sugar for the next month is $2 e. contract signed last month with large retail store that guarantees a minimum shelf space for grandpa's overloaded chocolate cookies for the next year

Alpine west, inc., operates a downhill ski area near lake tahoe, california. an all-day, adult ticket can be purchased for $55. adult customers also can purchase a season pass that entitles the pass holder to ski any day during the season, which typically runs from december 1 through april 30. the season pass is nontransferable, and the $450 price is nonrefundable. alpine expects its season pass holders to use their passes equally throughout the season. the company’s fiscal year ends on december 31. on november 6, 2009, jake lawson purchased a season ticket. required: 1. when should alpine west recognize revenue from the sale of its season passes? 2. prepare the appropriate journal entries that alpine would record on november 6 and december 31. 3. what will be included in the 2009 income statement and 2009 balance sheet related to the sale of the season pass to jake lawson?