To find: the optimal inventory level for each model, to find the optimal profit.
Answer to Problem 21CT
The optimal profit is $212000 and this occurs when there are 0 units model I and 5300 units model II are manufactured.
Explanation of Solution
Given information:
A manufacturer produces two models of television stands. The table at the left shows the times required for assembling, staining, and packaging the two models. The total times available for assembling, staining and packaging are 3750 hours, 8950 hours, and 2650 hours respectively. The profits per unit are $30 for model I and $40 for model II.
Calculation:
Let
The objective function is given as:
The constraints can be converted into inequalities as:
The area determines by the constraints is as shown below:
At the four vertices of the region formed by the constraints the objective function has the following values:
At
At
At
At
The optimal profit is $212000 and this occurs when there are 0 units model I and 5300 units model II are manufactured.
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