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Set up the following for solution by the simplex method. First express the linear constraints and objective function, then add slack variables to convert each constraint into a linear equation, and then set up the initial simplex tableau. A manufacturer of bicycles builds racing, touring, and mountain models. The bicycles are made of both aluminum and steel. The company has available 92,400 units of steel and 44,000 units of aluminum. The racing, touring, and mountain models need 18, 26, and 34 units of steel, and 19, 29, and 11 units of aluminum, respectively. How many of each type of bicycle should be made in order to maximize prot if the company makes $6 per racing bike, $13 per touring bike, and $25 per mountain bike? What is the maximum possible prot? Let x1, x2, and x3 be the numbers of racing, touring, and mountain bicycles, respectively. Express the linear constraints and objective function. V z= subject to: V 92,400 744,000 x V ,x V , with 1 2 x3 V (Do not factor. Do not include the $ symbol in your answers.) Add slack variables to convert each constraint into a linear equation. Select the correct choice below and ll in the answer boxes to complete your choice. C] A. 18x1 +26x2 +34x3 +51 = '33:? 3- 19x1 +29x2 +1'ix3 +s1 = 19x1+29x2+11x3+sz= 6x1+13x2+25x3+52= Cl 0- 19x1 + 29x2 +11x3 = + s1 C? 0- 18x1 + 26x2 + 34x3 = + s1 6x1+13x2+25x3= +52 19x1+29x2+11x3= +s2 C5 E- 18x1 + 26x2 + 34x3 = + s1 C? F- 18x1 + 26x2 + 34x3 + s1 = 6x1 +13x2 + 25x3 = + 52 6x1 +13x2 +25x3 + 52 = Set up the initial simplex tableau. X3 Z X2 S 1 S2 X1 92,400 44,000Use the simplex method to solve the linear programming Maximize Z = 10x1 + 15x2 problem. subject to: 12x1 + 3x, $ 42 5X1 + X, $ 20 3x1 + 3x, $ 48 with X1 20, X2 20 . . . Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. O A. The maximum is when x1 = , X2 = S1 S, = , and S3 = (Type integers or simplified fractions.) O B. There is no maximum.A company produces handmade shawls and afghans. They spin the yarn, dye it, and then weave it. A shawl requires 1 hour of spinning, 1 hour of dyeing, and 1 hour of weaving. An afghan requires 1 hour of spinning, 4 hours of dyeing, and 2 hours of weaving. There are at most 7 hours available each day for spinning, 12 hours for dyeing, and 8 hours for weaving. Complete parts a through c below. a. Complete the following table. Shawls Afghans Maximum Number of Hours Available Number X Hours Spinning 7 Hours Dyeing 12 Hours Weaving 8 (Type integers or decimals.) b. Set up a system of inequalities and graph the feasible region. Use the table to write a system of inequalities. $7 $ 12 S 8 x20 y20 (Simplify your answers. Use integers or decimals for any numbers in the expressions.) Choose the correct graph of the feasible region of this system of inequalities. O A. O B. O C. OD. X X X