AIRCRAFT LEASING. Consider the problem faced by Des Moines Airlines (DMA) in problem 35. Now suppose that the B77 aircraft actually requires 4 flight attendants rather than three.
a. Solve for the optimal solution to the (i) linear programming model and (ii) integer programming model.
b. Explain why the optimal solution in (ii) gives a smaller total seat capacity than that in (i).
35. AIRCRAFT LEASING. Des Moines Airlines (DMA) is a small new commuter airline that will locate its hub in Des Moines, Iowa. DMA plans to have 11 mechanics, 15 pilots, and 21 flight attendants available daily. DMA will be leasing two types of aircraft—the DM4 and the B77. The Federal Aviation Association’s (FAA’s) mandatory requirements for these aircraft are summarized in the following table. DMA’s objective is to maximize its total passenger capacity.
a. Formulate and graph a feasible region for this problem. Without knowing the seat capacity on each aircraft, why can we say for certain that the optimal solution to the linear programming model would also be the optimal solution to the integer linear programming model? (Hint: What are the possible optimal points for a linear programming model?)
b. The seat capacity is 25 for the DM4 and 70 for the B77. What is the optimal leasing plan for DMA?
c. If DMA must make do with one less worker to operate its fleet, should it be a mechanic, a pilot, or a flight attendant?
d. Excluding certain fixed costs (including pilot costs), each seat of fleet capacity gives DMA a net yearly profit of $25,000. If DMA plans to pay its pilots $110,000 per year, including benefits, should it hire an additional pilot?
e. DMA is considering redesigning the interior of the B77 to increase its seat capacity beyond 70. What is the maximum seating capacity for which the leasing plan found in part (a) remains optimal?
f. Suppose DMA could squeeze one more row of three seats into each of the two types of aircraft, increasing the seating capacity of the DM4 to 28 and the B77 to 73. Given no other changes in the assumptions of the problem, would the optimal leasing decision change? What practical considerations might you consider before implementing such a change?