Feasible Region All parts of this problem refer to the following feasible region and objective function.
- (a) Graph the feasible region.
- (b) On your graph from part (a), sketch the graphs of the linear equations obtained by setting P equal to 40, 36, 32, and 28.
- (c) If you continue to decrease the value of P, at which vertex of the feasible region will these lines first touch the feasible region?
- (d) Verify that the maximum value of P on the feasible region occurs at the vertex you chose in part (c).
Want to see the full answer?
Check out a sample textbook solutionChapter 10 Solutions
Precalculus: Mathematics for Calculus (Standalone Book)
- Use your schools library, the Internet, or some other reference source to find the real-life applications of constrained optimization.arrow_forwardFeasible region all part of this problem refer to the following Feasible region and objective function. {x0xyx+2y12x+y10}P=x+4y (a) Graph the Feasible region. (b) on your graph from part(a) , sketch the graph of the linear equation obtained by (c setting P equal to 40,36,32 and 28 . (c) if you continue to decrease the value of P, at which vertex of the Feasible region will these lines first touch the Feasible region . (d) verify that the maximum value of P on the Feasible region occurs at the vertices you too chose in part(c).arrow_forwardFeasible RegionAll parts of this problem refer to the following feasible region and objective function. {x0xyx+2y12x+y10 P=x+4y aGraph the feasible region. bOn your graph from part a, sketch the graphs of the linear equations obtained by setting P equal to 40, 36, 32, and 28. cIf you continue to decrease the value of P, at which vertex of the feasible region will these lines first touch the feasible region? dVerify that the maximum value of P on the feasible region occurs at the vertex you chose in part c.arrow_forward
- Making furniture Two woodworkers, Chase and Devin, get 100 for making a table and 80 for making a chair. On average, Chase must work 3 hours and Devin 2 hours to make a chair. Chase must work 2 hours and Devin 6 hours to make a table. If neither wishes to work more than 42 hours per week, how many tables and how many chairs should they make each week to maximize their income? Find the maximum income. Table Chair Time Available Devins Time hr 6 2 42 Chases Time hr 2 3 42 Income 100 80arrow_forwardA company manufactures two fertilizers, x and y. Each 50-pound bag of fertilizer requires three ingredients, which are available in the limited quantities shown in the table. The profit on each bag of fertilizer x is 6 and on each bag of y is 5. How many bags of each product should be produced to maximize the profit? Ingredient Number of Pounds in Fertilizer x Number of Pounds in Fertilizer y Total number of Pounds Available Nitrogen 6 10 20,000 Phosphorus 8 6 16,400 Potash 6 4 12,000arrow_forward
- College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage LearningAlgebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningCollege AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
- Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage