Suppose that a company needs new equipment, and that the machinery in question earns the company revenue at a continuous rate of 54000t 38000 dollars per year during the first six months of operation, and at the continuous rate of $65000 per year after the first six months. The cost of the machine is $140000. The interest rate is 5.75% per year, compounded continuously. a) Find the present value of the revenue earned by the machine during the first year of operation.
b) Determine how long it will take for the machine to pay for itself; that is, how long until the present value of the revenue is equal to the cost of the machine.

Astudent was asked to draw a demand and supply graph to illustrate the effect on the market for premium bottled water of a fall in the price of electrolyteselectrolytes used in some brands of premium bottled​ water, holding everything else constant. she drew the graph to the right and explained it as​ follows: ​"electrolyteselectrolytes are an input to some brands of premium bottled​ water, so a fall in the price of electrolyteselectrolytes will cause the supply curve for premium bottled water to shift to the right​ (from upper s 1s1 to upper s 2 right parenthesis .s2). because this shift in the supply curve results in a lower price left parenthesis upper p 2 right parenthesis commap2, consumers will want to buy more premium bottled water and the demand curve will shift to the right​ (from upper d 1d1 to upper d 2 right parenthesis .d2). we know that more premium bottled water will be​ sold, but we​ can't be sure whether the price of premium bottled water will rise or fall. that depends on whether the supply curve or the demand curve has shifted farther to the right. i assume that the effect on supply is greater than the effect on​ demand, so i show the final equilibrium price left parenthesis upper p 3 right parenthesisp3 as being lower than the initial equilibrium price left parenthesis upper p 1 right parenthesis .p1.​" where is the flaw in the​ student's argument? supply will shift inward. demand will not shift. demand will shift inward.