Consider the following five constraints x1 + 2x2 ≤ 3, x1 − x2 ≥ 0, 2x1 + x2 ≤ 3, x1 + 5x2 ≤ 6, x1 − 2x2 ≥ −1. (a) Sketch the feasible region and find the degenerate vertex x0. (b) How many possible working sets are there at x0? (c) Suppose that we wish to minimize x1 + x2 subject to these constraints, starting at x0 and using the simplex method. Find a working set A0 for which the Lagrange multiplier vector λ (the solution of AT 0 λ = c) contains at least one negative component λs, but the simplex search direction satisfying A0p = es is not a feasible descent direction. Draw a picture showing p emanating from x0. What are the blocking constraints? (d) Under the same conditions as in part (c), find a working set A¯ 0 for which the Lagrange multiplier vector contains at least one negative component, but the associated search direction ¯p is a feasible descent direction. Draw a picture showing ¯p emanating from x0. (e) Can you find a feasible descent direction at x0 if we wish instead to minimize −x1 − x2? Explain your answer.

Arriving and delivering a load of company executives for a business meeting at a destination far from home base requiring an overnight stay, a company’s pilot requested approval from the company finance office to pay to either have the company’s jet brought into the fbo's hangar overnight to protect it from a forecast snowfall or to have it de-iced by the fbo the following morning well-before scheduled departure. the company was under considerable financial pressure at the time, and the pilot’s requests were denied because of the cost. so, early the following morning, the pilot was up on the wing of the jet sweeping off an accumulation of snow and ice with a borrowed push broom in preparation for the scheduled departure with the executives, but slipped and fell to the ground, suffering a broken neck. the business was organized as a limited partnership, owned by 3 limited partners and one general partner. as a cost-saving measure, the company had dropped its workers’ compensation insurance before the accident. analyze the potential liability for the pilot’s injuries of each of the following, showing your reasoning clearly: the company the general partner the limited partners analyze how the outcome would have been different, if the business had been organized as a corporation and observed all of the formalities to legitimize its corporate status. analyze how the outcome would have been different, if the pilot had been covered by workers’ compensation insurance.

land, a building and equipment are acquired for a lump sum of $ 1,000,000. the market values of the land, building and equipment are $ 300,000, $ 800,000 and $ 300,000, respectively. what is the cost assigned to the equipment? (do not round any intermediary calculations, and round your final answer to the nearest dollar.)

Your uncle borrows $53,000 from the bank at 11 percent interest over the nine-year life of the loan. use appendix d for an approximate answer but calculate your final answer using the formula and financial calculator methods. what equal annual payments must be made to discharge the loan, plus pay the bank its required rate of interest