Math 504 - CST

Test 2

Duration: 75 minutes

This exam is worth of 30% of your Term 1 marks

- You are not allowed to use any other electronic devices

- You must show all your works (except multiple choices)

-You should graph all the equations with a ruler

- Remember that any form of plagiarism will result into a grade of "0"

GOOD LUCK!

Name: _______________________

Group: __________________

1. Multiple Choices Which graph below represents the solution set for the following system of inequalities? (2 pts)

• x ≥ 0

• y ≥ 0

• x ≥ 1

• y ≤ 3

A) C)

B) D)

2. Multiple Choices A company produces tables and chairs. The owner of the company must respect the constraints represented by the polygon below.

The following function C can be used to determine the total cost of production:

C = 45 x + 21y

How many tables and chairs must be produced in order to minimize the cost? (2 pts)

A) 10 tables and 20 chairs C) 30 tables and 40 chairs

B) 50 tables and 10 chairs D) 70 tables and 0 chair

3. Maria is going to buy flowers for his mother. The local florist sells red roses for $4.5 and white roses for $3.75. Maria will buy at least 5 flowers. However, she has a maximum budget of $62.

a) Identify the variables (1 pt)

Let x:

Let y:

b) Determine the system of constraints that describes this situation provided that

x ≥ 0 and y ≥ 0 (2 pts)

4. A polygon of constraints representing the solution for a system of inequalities is drawn in the Cartesian plane below. The coordinates of the vertices and some other points are shown on the graph below. Indicate in the table if a point is part of the solution (2 pts)

5. The system of inequalities and the polygon of constraints below are associated with the same optimizing situation. Each side of the polygon and its corresponding inequality are identified by the same number. What are the coordinates of the vertex A for this polygon of constraints? (2 pts)

Complete the following table.

No justification needed.

Points Write "yes" if this point is a solution and "no" if it is not

ABCDEFGH

6. Multiple Choices The following polygon of constraints represents the solution for an optimization situation that involves maximizing the profit of selling vanilla cookies and chocolate cookies.

The values in the following table were calculated in order to determine the profit.

Vertex ProfitA $32B $108C $108D $31

In this situation, how many solutions maximize the cost? (2 pts)

A) 1 solution C) 4 solutions

B) 2 solutions D) 7 solutions

7. Ana and Robert are full-time pilots at an aviation company. To ensure their safety, they have limited working hours for the day shift and the night shift.

The polygon below represents the constraints of their working time in one week.

where x: number of working hours during the day shift per week

y: number of working hours during the night shift per week

Their salary is $80 per day hour and $110 per night hour.

Ana made the maximum possible salary last week.

Robert drove 9 hours less than Ana did during the day shift and earned $3330 last week.

How many hours did Robert drive during the night shift last week? (4 pts)

Coordinates of the vertices of the polygon of constraints

A (15, 9)B (15, 21)C (18, 27)D (30, 21)

8. A swim team wants to minimize its transportation cost for a competition. It costs $150 to rent each van and $125 to rent each deluxe car. The following polygon of constraints represents the solutions for this situation.

where x: number of vans

y: number of deluxe cars

On the day of the competition, it is revealed that they must rent a minimum of 6 vehicles. Because of this, the minimum transportation cost will increase. By how much will the minimum transportation cost increase? (4 pts)

Coordinates of the vertices of the polygon of constraints

A (1, 3)B (3, 5)C (6, 2)D (4, 0)

9. The polygon of constraints below takes into account the operating constraints of the kitchen in a restaurant. Each cook is paid $150 per day, while every dish washer is paid $100 per day.

where x: number of cooks

y: number of dish washers

The restaurant hired new manager and he decides to adjust the salary of each cook to $110 per day and each dish washer to $140 per day.

Will the minimum daily cost of running the kitchen increase or decrease? (4 pts)

(Show all your works!)

10. Rose was in charge of buying snacks for a local fundraiser. She needs to respect the following constraints during the purchase:

• At most 200 more Oreos than Doritos.

• A minimum of 200 but not more than 500 Oreos.

• A minimum of 400 snacks.

• A maximum of 1000 snacks.

She bought Doritos for $3 each and Oreos for $2 each.

Let x represents the number of Doritos

Let y represents the number of Oreos.

What is the minimum purchasing cost? (5 pts)