
In Exercises 5-8, an objective function and a system of linear inequalities representing constraints are given.
a. Graph the system of inequalities representing the constraints.
b. Find the value of the objective function at each corner of the graphed region.
c. Use the values in part (b) to determine the maximum value of the objective function and the values of x and y for which the maximum occurs.
Objective Function
Constraints

Want to see the full answer?
Check out a sample textbook solution
Chapter 7 Solutions
Thinking Mathematically (6th Edition)
- (a) Let P be a point not on the line L that passes through the points Q and R. Show that the distance d from the point P to the line L is |a x bl |a| d where a = QR and b = QP. This answer has not been graded yet. (b) Use the formula in part (a) to find the distance from the point P(1, 1, 1) to the line through Q(0, 7, 6) and R(-1, 2, 6). 29.65arrow_forwardFind the area of the parallelogram with vertices K(1, 2, 2), L(1, 5, 4), M(6, 10, 4), and N(6, 7, 2).arrow_forwardFind the area of the parallelogram with vertices A(-5, 4), B(-3, 7), C(1, 5), and D(-1, 2).arrow_forward
- Find an equation of the plane. The plane through the point (8, 0, 4) and perpendicular to the line x = 3t, y = 6-t, z = 7 + 4tarrow_forwardFind an equation of the plane. The plane that passes through the line of intersection of the planes x-z=3 and y + 4z1 and is perpendicular to the plane x + y 2 = 4 5x+4y+3z 27 - Need Help? Read Itarrow_forwardFind the volume of the parallelepiped with adjacent edges PQ, PR, PS. P(3, 0, -2), Q(6, 2, 0), R(6, -1, 1), S(3, -3, 1) cubic units Need Help? Read It Watch Itarrow_forward
- Find a vector equation and parametric equations for the line. (Use the parameter t.) The line through the point (8, -5, 2) and parallel to the vector 2 - 3 r(t) = (x(t), y(t), z(t)) = (3,2.7,3.1)+(33, − 1) -arrow_forwardFind the cross product a x b. a = (t, t², t³), b = (1, 4t, 9t²)arrow_forwardFind the distance from the point to the given plane. (-3, 3, 2), x-2y-4z = 8arrow_forward
- Find the volume of the parallelepiped determined by the vectors a, b, and c. a = (6,2,-3), с b = (0, 3, 3), c = (6, -2, 4) cubic units Need Help? Read It Watch Itarrow_forwardFind the cosine of the angle between the planes x + y + z = 0 and x + 2y + 3z = 9.arrow_forwardFind a vector equation for the line segment from (3, -3, 4) to (7, 3, 1). (Use the parameter t.) r(t) = Need Help? Read It Watch Itarrow_forward
- College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage LearningAlgebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal LittellElementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageGlencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill




