For each of the following linear programming models, give your recommendation on which is the more efficient way (probably) to obtain an optimal solution: by applying the simplex method directly to this primal problem or by applying the simplex method directly to the dual problem instead. Explain. (a) Maximize Z= 10x1 - 4x2 + 7x3, subject to 3x - x2 + 2xz < 25 X1 - 2x2 + 3x3 = 25 5x + x2 + 2x3 = 40 x1 + x2 + x3 = 90 2x1 - x2 + x3 = 20 and x, 20, 20, x2 > 0. (b) Maximize Z = 2xy + 5x2 + 3x3 + 4X4 + X5, subject to x1 + 3x2 + 2x3 + 3x4 + x3 = 6 4x1 + 6x2 + 5xz + 7x4 + x3 = 15 and x; 20, for j = 1, 2, 3, 4, 5.

Fred smithers, a recent college graduate decided to open his own portable juice bar, smithers smoothies, to wheel around newport beach. you, a trusted friend of fred, are a business major that has also recently graduated and agreed to handle the books for a while to get some practical experience and have a favor that you can ask of fred in the future. given the following five transactions concerning the new venture, prepare the necessary journal entries for the transactions, post the journal entries to appropriate t accounts and prepare a trial balance as of the end of the month in order to answer to the necessary may 2: fred invests $12,000 of his own money to start the new company. this money was obtained from a part-time job working at a legal firm while he was in school. may 3: fred spent $5,100 cash to purchase a refrigerated trailer that he can pull behind his car and set up at the beach. under your advice, fred agrees to place the new asset under an account called "equipment." may 6: fred bought $640 of supplies on account from the flav-o-rite confectioners company. because they will last longer than a single accounting period fred agrees to record them as, "supplies" as per your suggestion. may 13: fred sat on the beach for six hours without a single sale and was feeling very down. right before he left, however, a plumber escorting his family reunion along the beach stopped by his stand and bought $800 worth of smoothies for the entire family. under your advice, fred agrees to call this cash revenue, "sales." may 15: excited about his new venture, fred withdraws $350 from the company to take his girlfriend out to dinner. what would be the balance in the cash account at the end of the period following the posting of all the transactions?