Question

The Fly-Right Airplane Company builds small jet airplanes to sell to corporations for the use of their executives. To meet the needs of these executives, the company’s customers sometimes order a custom design of the airplanes being purchased. When this occurs, a substantial start-up cost is incurred to initiate the production of these airplanes. Fly-Right has recently received purchase requests from three customers with short deadlines. However, because the company’s production facilities already are almost completely tied up filling previous orders, it will not be able to accept all three orders. Therefore, a decision now needs to be made on the number of airplanes the company will agree to produce (if any) for each of the three customers. The relevant data are given in the next table. The first row gives the start-up cost required to initiate the production of the airplanes for each customer. Once the production is under way, the marginal net revenue (which is the purchase price minus the marginal production cost) from each airplane produced is shown in the second row. The third row gives the percentage of the available production capacity that would be used for each airplane produced. The last row indicates the maximum number of airplanes requested by each customer (but less will be accepted). Customer 1 2 3 Start-up cost $3 million $2 million 0 Marginal net revenue $2 million $3 million $0.8 million Capacity used per plane 20% 40% 20% Maximum order 3 planes 2 planes 5 planes Fly-Right now wants to determine how many airplanes to produce for each customer (if any) to maximize the company’s total profit (total net revenue minus start-up costs). Formulate a model with both integer variables and binary variables for this problem.

The Fly-Right Airplane Company builds small jet airplanes to sell to corporations for the use of their executives. To meet the needs of these executives, the company’s customers sometimes order a custom design of the airplanes being purchased. When this occurs, a substantial start-up cost is incurred to initiate the production of these airplanes. Fly-Right has recently received purchase requests from three customers with short deadlines. However, because the company’s production facilities already are almost completely tied up filling previous orders, it will not be able to accept all three orders. Therefore, a decision now needs to be made on the number of airplanes the company will agree to produce (if any) for each of the three customers. The relevant data are given in the next table. The first row gives the start-up cost required to initiate the production of the airplanes for each customer. Once the production is under way, the marginal net revenue (which is the purchase price minus the marginal production cost) from each airplane produced is shown in the second row. The third row gives the percentage of the available production capacity that would be used for each airplane produced. The last row indicates the maximum number of airplanes requested by each customer (but less will be accepted).

Customer
1 2 3
Start-up cost $3 million $2 million 0
Marginal net revenue $2 million $3 million $0.8 million
Capacity used per plane 20% 40% 20%
Maximum order 3 planes 2 planes 5 planes

Fly-Right now wants to determine how many airplanes to produce for each customer (if any) to maximize the company’s total profit (total net revenue minus start-up costs). Formulate a model with both integer variables and binary variables for this problem.

The Fly-Right Airplane Company builds small jet airplanes to sell to corporations for the use of their executives. To meet the needs of these executives, the company’s customers sometimes order a custom design of the airplanes being purchased. When this occurs, a substantial start-up cost is incurred to initiate the production of these airplanes. Fly-Right has recently received purchase requests from three customers with short deadlines. However, because the company’s production facilities already are almost completely tied up filling previous orders, it will not be able to accept all three orders. Therefore, a decision now needs to be made on the number of airplanes the company will agree to produce (if any) for each of the three customers. The relevant data are given in the next table. The first row gives the start-up cost required to initiate the production of the airplanes for each customer. Once the production is under way, the marginal net revenue (which is the purchase price minus the marginal production cost) from each airplane produced is shown in the second row. The third row gives the percentage of the available production capacity that would be used for each airplane produced. The last row indicates the maximum number of airplanes requested by each customer (but less will be accepted).

Customer
1 2 3
Start-up cost 3 million2 million 0
Marginal net revenue 2 million3 million 0.8 million
Capacity used per plane 20% 40% 20%
Maximum order 3 planes 2 planes 5 planes

Fly-Right now wants to determine how many airplanes to produce for each customer (if any) to maximize the company’s total profit (total net revenue minus start-up costs). Formulate a model with both integer variables and binary variables for this problem.

Added by Nicholas W.

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