If a decision variable is not positive in the optimal solution, its reduced cost is Group of answer choices its dual price. the amount its objective function value would need to improve before it could become positive. what its objective function value would need to be before it could become positive. zero.

Ursus, inc., is considering a project that would have a five-year life and would require a $1,650,000 investment in equipment. at the end of five years, the project would terminate and the equipment would have no salvage value. the project would provide net operating income each year as follows (ignore income taxes.):

Bonds often pay a coupon twice a year. for the valuation of bonds that make semiannual payments, the number of periods doubles, whereas the amount of cash flow decreases by half. using the values of cash flows and number of periods, the valuation model is adjusted accordingly. assume that a $1,000,000 par value, semiannual coupon us treasury note with three years to maturity has a coupon rate of 3%. the yield to maturity (ytm) of the bond is 7.70%. using this information and ignoring the other costs involved, calculate the value of the treasury note:

Arnold rossiter is a 40-year-old employee of the barrington company who will retire at age 60 and expects to live to age 75. the firm has promised a retirement income of $20,000 at the end of each year following retirement until death. the firm's pension fund is expected to earn 7 percent annually on its assets and the firm uses 7% to discount pension benefits. what is barrington's annual pension contribution to the nearest dollar for mr. rossiter? (assume certainty and end-of-year cash flows.)