To determine To calculate: The minimum value of the equation w = 5 x + 2 y , subject to: x + y ≤ 50 2 x + y ≥ 20 x + 2 y ≥ 30 x ≥ 0 And, y ≥ 0 Explanation Given: The function to be minimized is w = 5 x + 2 y subject to: x + y ≤ 50 2 x + y ≥ 20 x + 2 y ≥ 30 x ≥ 0 And, y ≥ 0 Formula used: The corner point theorem states that if a feasible region is bounded, then the objective function has both a maximum value as well as a minimum value and both occur at one or more corner points. If the feasible region is unbounded, the objective function may not have a maximum value or minimum value but if a maximum or minimum value exists, it will occur at one or more corner points. Calculation: The constraints represented in the form of linear inequalities are: x + y ≤ 50 2 x + y ≥ 20 x + 2 y ≥ 30 x ≥ 0 And, y ≥ 0 The x − intercept for the equation, x + y = 50 . x + 0 = 50 x = 50 The y − intercept for the equation, x + y = 50 . y + 0 = 50 y = 50 Substitute ( 0 , 0 ) in the inequality, x + y ≤ 50 . x + y ≥ 50 0 ≥ 50 Since, the above inequality does not hold true for ( 0 , 0 ) . Thus, the feasible region is away from the origin for the inequality, x + y ≤ 50 . The x − intercept for the equation, 2 x + y = 20 . 2 x + 0 = 20 2 x = 20 x = 10 The y − intercept for the equation, 2 x + y = 20 . y + 2 ( 0 ) = 20 y = 20 Substitute ( 0 , 0 ) in the inequality, 2 x + y ≥ 20 . 2 ( 0 ) + ( 0 ) ≥ 20 0 ≥ 20 Since, the above inequality does not hold true for ( 0 , 0 ) . Thus, the feasible region is away from the origin for the inequality, 2 x + y ≥ 20

MATH W/APPLICAT.W/NOTES GDE +ACCESS CODE

11th Edition

ISBN: 9781323751671

Author: Lial

Publisher: PEARSON C

See similar textbooks

Videos

Question

Chapter 7, Problem 15RE

To determine

To calculate: The minimum value of the equation w=5x+2y, subject to:

x+y≤502x+y≥20x+2y≥30x≥0

And,

y≥0

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 7, Problem 14RE

Chapter 7, Problem 16RE

Students have asked these similar questions

16. Solve the given differential equation: y" + 4y sin (t)u(t 2π), - y(0) = 1, y'(0) = 0 Given, 1 (x² + 1)(x²+4) 1/3 -1/3 = + x²+1 x² +4 Send your answer in pen and paper don't r eputed ur self down Don't send the same previous answer that was Al generated Don't use any Al tool show ur answer in pe n and paper then take

R denotes the field of real numbers, Q denotes the field of rationals, and Fp denotes the field of p elements given by integers modulo p. You may refer to general results from lectures. Question 1 For each non-negative integer m, let R[x]m denote the vector space consisting of the polynomials in x with coefficients in R and of degree ≤ m. x²+2, V3 = 5. Prove that (V1, V2, V3) is a linearly independent (a) Let vi = x, V2 = list in R[x] 3. (b) Let V1, V2, V3 be as defined in (a). Find a vector v € R[×]3 such that (V1, V2, V3, V4) is a basis of R[x] 3. [8] [6] (c) Prove that the map ƒ from R[x] 2 to R[x]3 given by f(p(x)) = xp(x) — xp(0) is a linear map. [6] (d) Write down the matrix for the map ƒ defined in (c) with respect to the basis (2,2x + 1, x²) of R[x] 2 and the basis (1, x, x², x³) of R[x] 3. [5]

Question 4 (a) The following matrices represent linear maps on R² with respect to an orthonormal basis: = [1/√5 2/√5 [2/√5 -1/√5] " [1/√5 2/√5] A = B = [2/√5 1/√5] 1 C = D = = = [ 1/3/5 2/35] 1/√5 2/√5 -2/√5 1/√5' For each of the matrices A, B, C, D, state whether it represents a self-adjoint linear map, an orthogonal linear map, both, or neither. (b) For the quadratic form q(x, y, z) = y² + 2xy +2yz over R, write down a linear change of variables to u, v, w such that q in these terms is in canonical form for Sylvester's Law of Inertia. [6] [4]

Chapter 7 Solutions

MATH W/APPLICAT.W/NOTES GDE +ACCESS CODE

Ch. 7.1 - Checkpoint 1 Graph the given...Ch. 7.1 - Prob. 2CP Ch. 7.1 - Prob. 3CP Ch. 7.1 - Prob. 4CP Ch. 7.1 - Prob. 5CP Ch. 7.1 - Checkpoint 6 Graph the feasible region of the...Ch. 7.1 - Prob. 7CP Ch. 7.1 - Match the inequality with its graph, which is one...Ch. 7.1 - Match the inequality with its graph, which is one...Ch. 7.1 - Match the inequality with its graph, which is one...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

The minimum value of the equation w = 5 x + 2 y , subject to: x + y ≤ 50 2 x + y ≥ 20 x + 2 y ≥ 30 x ≥ 0 And, y ≥ 0

Videos

To calculate: The minimum value of the equation w=5x+2y, subject to: x+y≤502x+y≥20x+2y≥30x≥0 And, y≥0

Want to see the full answer?

Chapter 7 Solutions

To calculate: The minimum value of the equation w=5x+2y, subject to:

x+y≤502x+y≥20x+2y≥30x≥0

And,

y≥0