need help with #46 and #47

LINEAR PROGRAMMING: COMPUTER SOLUTION AND SENSITIVITY ANALYSIS b. If Food Max could get the local dairy to increase the amount of milk it could supply cach week, would it increase profit? c. Food Max is considering discounting its own brand to increase sales. If it were to do so, it would decrease the profit margin for its own brand to S0.86 per carton, but it would cut the demand for the national brand relative to its own brand in half. Discuss whether the store should implement the price discount. 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 S1.700, 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 Hoke's 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? e. If John purchased a cheaper cross-country bike for $1.200 and sold it for $1,900, would this affect the original solution? 48. Metro Food Services Company delivers fresh sandwiches each morning to vending machines throughout the city. The company makes three kinds of sandwiches-ham and cheese, bolo gna, and chicken salad. A ham and cheese sandwich requires a worker 0.45 minutes to asse a bologna sandwich requires 0.41 minutes, and a chicken salad sandwich requires 0.50 to make. The company has 960 available minutes each night for sandwich assembly. machine capacity is available for 2,000 sandwiches each day. The profit for a ham e sandwich is $0.35, the profit for a bologna sandwich is $0.42, and the profit for