1) Maximize = 71 + 22 + 53

subject to the constraints

51 + 42 + 83 200

82 + 33 45

63 35

1 0, 2 0, 3 0.

2) Introduce slack variables and set up the initial simplex tableau.

Find the dual problem:

Minimize = 231 + 102

subject to the constraints

21 + 22 160

31 + 72 170

51 + 42 50

1 0, 2 0.

3) A borrower signs a note for a discounted loan and agrees to pay the lender $1000 in 22 months at a 5.5% rate of interest. How much does the borrower receive?

4) Find the annual payment required to save $50,000 after 6 years, if you place the money in an account paying4% per annum compounded annually.

5) The U.S. Census Bureau reported that 255,143,000 Americans were covered by health insurance in the year 2008 and 46,340,000 Americans were not covered by health insurance that year. What is the probability a randomly selected American in the year 2008 was covered by health insurance?

Write the answer as a decimal rounded to three decimal places.