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 92,300 units of steel and 42,000 units of aluminum. The racing, touring, and mountain models need 13, 21, and 33 units of steel, and 15, 28, and 18 units of aluminum, respectively. How many of each type of bicycle should be made in order to maximize profit if the company makes $9 per racing bike, $18 per touring bike, and $24 per mountain bike? What is the maximum possible profit? Question content area bottom Part 1 Let x 1, x 2, and x 3 be the numbers of racing, touring, and mountain bicycles, respectively. Express the linear constraints and objective function. Maximize zequals select: 9x1 + 18x2 + 24x3 9 x 1 plus 18 x 2 plus 24 x 3 subject to: select: 13x1 + 21x2 + 33x3 + s1 13 x 1 plus 21 x 2 plus 33 x 3 plus s 1 equals 92,300 select: 92,300 15x1 + 28x2 + 18x3 + s2 92,300 15 x 1 plus 28 x 2 plus 18 x 3 plus s 2 equals 42,000 with x 1 greater than enter your response here, x 2 greater than enter your response here, x 3 greater than enter your response here (Do not factor. Do not include the $ symbol in your answers.)