A bus company which operates a fleet of 80 buses, needs to determine the optimal mix of small, medium and large buses for its fleet. To satisfy customer requirement a minimum of 10% of the fleet must be large buses that can carry 50 passengers. There is no minimum requirement for small or medium buses which seat 30 and 40 passengers respectively, but the fleet must be able to accommodate at least 3,000 passengers at any given time. The following table contains information on the daily running costs (in dollars), the pollution rating and the safety rating of each of the three bus types. The pollution rating is on a scale of 1 to 10 where 1 reflects the best environmental outcome. The safety rating is also on a scale of 1 to 10 with 10 being the score for the safest bus. Bus Cost per day Pollution rating Safety score Large Medium Small $490 $440 $400 a. Determine the fleet mix that minimizes costs. What is the cost, the mean pollution rating and the mean safety score for this fleet? (6 marks) b. Determine the fleet mix that minimizes the mean pollution rating. What is the cost, the mean pollution rating and the mean safety score for this fleet? (6 marks) c. Determine the fleet mix that maximizes the mean safety. What is the cost, the mean pollution rating and the mean safety score for this fleet? (6 marks) d. Formulate a goal programming model with a MINIMAX objective function which assumes that the company values safety 50% more than costs and 100% more than pollution considerations. (8 marks) e. Solve problem using Excel Solver. Provide a screenshot of your spreadsheet and explain your results. (8 marks) A bus company which operates a fleet of 80 buses, needs to determine the optimal mix of small, medium and large buses for its fleet. To satisfy customer requirement a minimum of 10% of the fleet must be large buses that can carry 50 passengers. There is no minimum requirement for small or medium buses which seat 30 and 40 passengers respectively, but the fleet must be able to accommodate at least 3,000 passengers at any given time. The following table contains information on the daily running costs (in dollars), the pollution rating and the safety rating of each of the three bus types. The pollution rating is on a scale of 1 to 10 where 1 reflects the best environmental outcome. The safety rating is also on a scale of 1 to 10 with 10 being the score for the safest bus. Bus Cost per day Pollution rating Safety score Large Medium Small $490 $440 $400 a. Determine the fleet mix that minimizes costs. What is the cost, the mean pollution rating and the mean safety score for this fleet? (6 marks) b. Determine the fleet mix that minimizes the mean pollution rating. What is the cost, the mean pollution rating and the mean safety score for this fleet? (6 marks) c. Determine the fleet mix that maximizes the mean safety. What is the cost, the mean pollution rating and the mean safety score for this fleet? (6 marks) d. Formulate a goal programming model with a MINIMAX objective function which assumes that the company values safety 50% more than costs and 100% more than pollution considerations. (8 marks) e. Solve problem using Excel Solver. Provide a screenshot of your spreadsheet and explain your results. (8 marks)
