In this worksheet, we will practice finding the optimal solution of a linear system that has an objective function and multiple constraints.

**Q4: **

Given the graph below and that , , , and , determine at which point the function has its maximum using linear programming.

- A
- B
- C
- D

**Q5: **

Using linear programming, find the minimum and maximum values of the function given that , , , and .

- AThe minimum value is , and the maximum value is 1.
- BThe minimum value is , and the maximum value is .
- CThe minimum value is 0, and the maximum value is 9.
- DThe minimum value is , and the maximum value is 1.

**Q6: **

Minimize subject to the constraints , , and .

- A9
- B7
- C1
- D2
- E18

**Q7: **

Consider the following inequalities in the nonnegative variables , , and : Find the maximum and minimum possible values of subject to these constraints.

- Aminimum: , maximum: 5
- Bminimum: , maximum: 5
- Cminimum: , maximum: 7
- Dminimum: , maximum: 7
- Eminimum: , maximum: 5

**Q8: **

Consider the following inequalities in the nonnegative variables , , and : Find the maximum and minimum possible values of subject to these constraints.

- Aminimum: , maximum: 7
- Bminimum: , maximum: 6
- Cminimum: , maximum: 6
- Dminimum: , maximum: 7

**Q9: **

Consider the following inequalities in the nonnegative variables , , and : Find the maximum and minimum possible values of subject to these constraints.

- Aminimum: 0, maximum: 7
- Bminimum: 1, maximum: 7
- Cminimum: 1, maximum: 14
- Dminimum: 0, maximum: 14

**Q10: **

- Aminimum: , maximum: 7
- Bminimum: , maximum: 6
- Cminimum: , maximum: 6
- Dminimum: , maximum: 7

**Q11: **

- Aminimum: 0, maximum:
- Bminimum: 1, maximum:
- Cminimum: 1, maximum: 7
- Dminimum: 0, maximum: 7

**Q12: **

Which of the following points is a solution to the system of inequalities , , , and ?

- A
- B
- C
- D
- E

**Q13: **

Which of the following points belongs to the solution set of the two inequalities and ?

- A
- B
- C
- D
- E

**Q14: **

If the point , where is located in the second quadrant, find .

**Q15: **

The solution set of the inequalities and lies in which quadrant?

- Athird
- Bsecond
- Cforth
- Dfirst

**Q16: **

When hired at a new job selling electronics, you are given two pay options:

- Option A: a base salary of a year with a commission of of your sales
- Option B: a base salary of a year with a commission of of your sales

How many dollarsβ worth of electronics would you need to sell for option A to produce a larger income?

- Amore than
- Bmore than
- Cmore than
- Dmore than