Each problem on an exam is worth 20 points. suppose that from the last seconds you devoted to problem 10 on the exam you earned 2 extra points, while from the last seconds devoted to problem 8 you earned 4 extra points. the total number of points you earned on these two problems were 8 and 6, respectively, and the total time you spent on each was the same. how—if at all—should you have reallocated your time between them?

You are the manager of a large crude-oil refinery. as part of the refining process, a certain heat exchanger (operated at high temperatures and with abrasive material flowing through it) must be replaced every year. the replacement and downtime cost in the first year is $165 comma 000. this cost is expected to increase due to inflation at a rate of 7% per year for six years (i.e. until the eoy 7), at which time this particular heat exchanger will no longer be needed. if the company's cost of capital is 15% per year, how much could you afford to spend for a higher quality heat exchanger so that these annual replacement and downtime costs could be eliminated?