Free Printable Objective Function

1.

Write the objective function:

A student earns $15 per hour for tutoring and $10 per hour as a teacher's aid. Let x = the number of hours each week spent tutoring and y = the number of hours each week spent as a teacher's aid. Let z represent the total weekly earnings.

(a) (b) (c) (d) + (e)

Choose from the below words

z

=

15

x

10y

15y

-

10

2.

Write the objective equation that models the total monthly profit.

A television manufacturer makes QLED and OLED televisions. The profit per unit is $125 for QLED televisions and $200 for the OLED televisions. Let x = the number of QLED televisions manufactured in a month and let y = the number of OLED televisions manufactured in a month.

a)

z = 200x + 125y

b)

z = 125x + 200y

c)

z = 125 + 200y

d)

z = 125x + 200

3.

Using the objective function: R=-2x - 4y what is the value for pont D?

a)

12

b)

-20

c)

-12

d)

20

4.

Using the objective function: P=8.5x + 12y what is the value for pont R?

a)

126.5

b)

119.5

c)

137

d)

132.5

5.

Use the function f(x) = 7n + 96 to complete the table

a)

18

b)

96

c)

131

d)

7

e)

54

1

2

3

1)

2)

3)

6.

Using the objective function:

C=5x - 7y

what is the value for pont P?

a)

-9

b)

4

c)

19

d)

-17

7.

Given the objective function:

M=-3x + 2y

at what point do you get your minimum value?

a)

S

b)

R

c)

Q

d)

U

e)

T

8.

Given the objective function:

M=-3x + 2y

at what point do you get your maximum value?

a)

N

b)

O

c)

P

9.

Given the objective function: P = 30x + 50y

Which vertex maximizes the profit?

a)

(0,0)

b)

(6,2)

c)

(8,0)

d)

(0,6)

10.

Find the values of x and y that maximize the objective function P = 3x + 2y for the graph. What is the maximum value?

a)

maximum value at (5, 4); 32

b)

maximum value at (0, 8); 16

c)

maximum value at (9, 0); 27

d)

maximum value at (0, 0); 0

11.

Sarah makes $30 for each small purse (x) and $50 for each big purse (y). What is the objective quantity?

a)

P = 30x + 50y

b)

P = 50x + 30y

12.

Objective quantity:
P = 30x + 50y
Corner that maximizes profit: (0, 6)
What is the profit?

a)

300

b)

280

c)

400

d)

240

13.

Consider the following optimization problem, in which a function δ has to be minimized.

a)

The solution does not exist because the problem is unbounded.

b)

The solution does not exist because no feasible points exist.

c)

The solution is x₁ = 10 and x₂ = 10/7.

14.

The generic optimization problem (P) is convex if the objective function and all __________ _________ are convex.

(a)

15.

When the feasible set is bounded and closed, a solution to the optimization problem always exists.

a)

This is true for any continuous objective function, not necessarily convex

b)

This is true for any objective function, not necessarily convex

c)

This is only true for convex objective functions

d)

This is never true

16.

Which corner point will maximize the Objective Function
$Z\ =\ 5x\ +\ 2y$

a)

(7,4)

b)

(3,10)

c)

(10,1)

d)

(8,5)

17.

Sarah makes $30 for each small purse (x) and $50 for each big purse (y). What is the objective function?

a)

P = 30x + 50y

b)

P = 50x + 30y

18.

A farmer can plant up to 6 acres of land with soybeans and corn. Her use of a necessary pesticide is limited by federal regulations to 15 gallons for her entire 6 acres. Soybeans require 2 gallons of pesticide for every acre planted and corn requires 3 gallons per acre. The profit the farmer makes by earning $4,000 for every acre of soybeans he plants and $3,000 for every acre he plants with barley can be modeled by P=4000x+3000y . What is the maximum profit that she can earn?

a)

$15,000

b)

$21,000

c)

$18,000

d)

$25,000

19.

A farmer can plant up to 6 acres of land with soybeans and corn. Her use of a necessary pesticide is limited by federal regulations to 15 gallons for her entire 6 acres. Soybeans require 2 gallons of pesticide for every acre planted and corn requires 3 gallons per acre. The profit the farmer makes by earning $4,000 for every acre of soybeans he plants and $3,000 for every acre he plants with barley can be modeled by P=4000x+3000y . What combination of soybeans and corn will maximize profit?

a)

4 acres of soybeans and 2 acres of corn

b)

6 acres of soybeans and 0 acres of corn

c)

3 acres of soybeans and 3 acres of corn

d)

0 acres of soybeans and 5 acres of corn

20.

Maximize P = 3x + y with the following constraints:

$x+y\ \le300$

$y\ \ge100$

$x\ \le150$

a)

x = 0, y = 300

b)

x = 150, y = 150

c)

x = 100, y 150

d)

x = 150, y = 100

Objective Function

Total questions: 20

Worksheet time: 20mins

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