To find: the optimal inventory level for the model, to find the optimal profit.
Answer to Problem 37E
The optimal profit is $8295 and the optimal inventory level is 230 units of $225 model and 45 units of $250 model.
Explanation of Solution
Given:
A merchant plans to sell two models of MP3 players at prices of $225 and $250. The $225 model yield a profit of $30 per unit and the $250 model yields a profit of $31 per unit. The merchant estimates that the total monthly demand will not exceed 275 units. The maximum investment is $63000 in inventory for these products.
Calculation:
Let
The two constraints can be converted into linear inequalities as:
Since the number of pieces produced cannot be negative, we can get two more constraints of
The area bounded by the constraints are shown below:
Now, to find the co-ordinates of the point A where the two lines intersect. The lines are:
From equation (1),
From equation (2),
At the intersection point
So the co-ordinates of the intersection point is
At the four vertices of the region formed by the constraints the objective function has the following values:
At
At
At
At
So the optimal profit is $8295 and the optimal inventory level is 230 units of $225 model and 45 units of $250 model.
Chapter 7 Solutions
EBK PRECALCULUS W/LIMITS
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning