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22. Solve the linear programming model formulated in Problem 21 for Rucklehouse Public Relations graphically. a. Determine the sensitivity ranges for the daily cost of a telephone interviewer and the number of personal interviews required. b. Does the firm conduct any more telephone and personal interviews than are required, and if so, how many more? c. What would be the effect on the optimal solution if the firm was required by the client to increase the number of personal interviews conducted from 800 to a total of 1,200? 23. Solve the linear programming model formulated in Problem 21 for Rucklehouse Public Relations by using the computer. a. If the firm could reduce the minimum interview requirement for either telephone or personal interviews, which should the firm select? How much would a reduction of one interview in the requirement you selected reduce total cost? Solve the model again, using the computer, with the reduction of this one interview in the constraint requirement to verify your answer. b. Identify the sensitivity ranges for the cost of a personal interview and the number of total interviews required. 46. John Hoke owns Hoke's Spokes, a bicycle shop. Most of John's bicycle sales are customer orders; however, he also stocks bicycles for walk-in customers. He stocks three types of bicycles-road- racing, cross-country, and mountain. A road-racing bike costs $1,200, a cross-country bike costs $1,700, and a mountain bike costs $900. He sells road-racing bikes for $1,800, cross-country bikes for $2,100, and mountain bikes for $1,200. He has $12,000 available this month to purchase bikes. Each bike must be assembled; a road-racing bike requires 8 hours to assemble, a cross-country bike requires 12 hours, and a mountain bike requires 16 hours. He estimates that he and his employees have 120 hours available to assemble bikes. He has enough space in his store to order 20 bikes this month. Based on past sales, John wants to stock at least twice as many mountain bikes as the other two combined because mountain bikes sell better. Formulate a linear programming model for this problem. 47. Solve the linear programming model formulated in Problem 46 for Hokes Spokes by using the computer. a. Should John Hoke try to increase his budget for purchasing bikes, increase space to stock bikes, or increase labor hours to assemble bikes? Why? b. If John hired an additional worker for 30 hours at $10 per hour, how much additional profit would he make, if any? c. If John purchased a cheaper cross-country bike for $1,200 and sold it for $1,900, would this affect the original solution