The trump russian doll corporation (trdc) produces four types of dolls, where doll numbers 1, 2, 3, and 4 earn profits of $8, $14, $20, and s30, respec- tively. each doll is subjected to four processes: plasti-casting, mold-vibrating, hand-painting, and inspection. the plant manager plans to maximize profits during the next month. during this period, she has 800 hours available for plasti-casting, 1000 hours available on the mold-vibrator, and 340 hours of in spection time. hand-painting time is unconstrained. she formulates an lp problem (p) with the following initial tableau 2 8r 14r 20z3- 30r 1,511 + 2t9 + 4zg + 5x4 0.511 + 0.6t2 + z3 + 2x4 800 1000 +7340 here, z? , z2, z3, and t1 represent the number of dolls of types 1, 2, 3, and 4. after solving by the simplex method, the final tableau is: 38r360r5r5 26 6000 200 = 400 2 t2 11r3 + 191.5a5 123> 22m 0.4r3 1.640.1.x5- answer the following questions, by hand computations; you may use the opl software to check your work but you need not submit any of the opl files (a) write down the basic solution of the tableau. find an optimal solution y* to the dual of (p), and use it to check that x* is optimal (b) suppose that the profit earned by dolls of type 3 increases from $20 to $60. does the basis b- 2,1,7 stay optimal? if not, begin to solve the new problem; go as far as identifying the leaving and entering variable for the first iteration c) find the range of values for the profit a earned by dolls of type 1 such that the basis b-(2,1,7) remains optimal (note that ? 8 for (p)) (d) assume that trdc may also produce doll houses, each of which requires 50 hours of plasti-casting, 10 hours of mold-vibrating, and 5 hours of inspec- tion time (the time for hand-painting is not relevant). find the minimum profit for the dol houses such that trdc would produce some doll houses. (e) determine the range of values for the number ? of hours of inspection time for which the basis b {2,1,7} remains optimal (note that ? 340 for (f) suppose that the available time on the mold-vibrator decreases from 1000 hours to 900 hours. solve this variation of (p), starting from the given optimal