Optimization Challenges for Students

Optimization Challenges for Students

12th Grade

12 Qs

quiz-placeholder

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Optimization Challenges for Students

Optimization Challenges for Students

Assessment

Quiz

Others

12th Grade

Practice Problem

Hard

Created by

Adane Yitbarek

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12 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the maximum value of the function f(x) = -2x^2 + 4x + 1 within the interval [0, 3]?

1

4

2

3

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Minimize the cost function C(x) = 5x + 3 subject to the constraint x ≥ 2. What is the minimum cost?

10

20

13

15

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Given the linear programming problem, maximize z = 3x + 4y subject to the constraints x + 2y ≤ 8 and x ≥ 0, y ≥ 0. What is the maximum value of z?

16

10

20

12

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

A farmer wants to fence a rectangular area of 200 square meters. What dimensions will maximize the area if the length is twice the width?

Length: 25 meters, Width: 12.5 meters

Length: 15 meters, Width: 5 meters

Length: 20 meters, Width: 10 meters

Length: 30 meters, Width: 15 meters

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Find the minimum value of the function g(x) = x^2 - 6x + 10. What is the minimum value and at which x does it occur?

Minimum value is 1 at x = 3.

Minimum value is 0 at x = 1.

Minimum value is 4 at x = 2.

Minimum value is 2 at x = 4.

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Maximize the profit function P(x) = 50x - 2x^2 under the constraint that x ≤ 20. What is the maximum profit?

312.5

400

300

250

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

A company produces two products A and B. The profit from A is $5 and from B is $7. If the production constraints are 3A + 2B ≤ 12, what is the maximum profit?

35

50

42

28

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