A small bicycle manufacturer in Mississauga wants to start to make two new types of electric bicycles.
Question:
A small bicycle manufacturer in Mississauga wants to start to make two new types of electric bicycles. Each type of electric bicycle will require assembly time, inspection time, and storage space. The amounts of each of these resources that can be devoted to the production of these bicycles are limited. The manager of the firm would like to determine the quantity of each type of bicycle to produce in order to maximize the profit generated by sales of these. In order to develop a suitable model of the problem, the manager has met with the design and manufacturing personnel. As a result of those meetings, the manager has obtained the following information:
The manager met with the firm's marketing manager and learned that demand for the bicycles was such that whatever combination of these two types of bicycles is produced, all of the output can be sold at the determined prices.
We will need two decision variables (Note: They do NOT need be integers, as the production is continuous over many days.):
- x: number of bicycles of type 1 to produce per day (Hint: plot this on the horizontal axis)
- y: number of bicycles of type 2 to produce per day (Hint: plot this on the vertical axis)
Solve the problem graphically. You do not need to actually draw the figure here, but do it on a piece of math paper instead (does not need to be submitted). The origin (0,0) will be the first corner point of the feasible region. In total you should have 5 corner points. List the remaining corner points in CLOCKWISE order after the origin.
1. State the x and y coordinates of the second corner and third corner (Note: This does NOT need to be an integer, as the production is continuous over many days). Please round to 2 decimal places.
2. State the x and y coordinates of the forth corner and fifth corner (Note: This does NOT need to be an integer, as the production is continuous over many days). Please round to 2 decimal places.
3. State the x and y coordinate of the optimal corner point (Note: This does NOT need to be an integer, as the production is continuous over many days). Please round to 2 decimal places.
4. State the profit at the optimal corner.
International Marketing And Export Management
ISBN: 9781292016924
8th Edition
Authors: Gerald Albaum , Alexander Josiassen , Edwin Duerr