Finding Solutions of Linear Inequalities in Two Variables

Abigail, Ethan, and Ava are planning a trip and they have different constraints on their budgets, time, and destinations. How do they determine a common solution to their system of inequalities?

• They graph each person's constraints and find the overlapping region that satisfies all

• They ignore the inequalities and find the average of their constraints

• They use trial and error to find a random solution that might satisfy all

• They solve a single person's constraints and apply the solution to the other people's constraints

Colin needs to save at least $200 for homecoming. He works 2 jobs earning $9/hour at Wawa and $25/hour mowing lawns. He only has time to work 16 hours before homecoming.

• x + y ≥ 25

  x + y ≤ 9

• 100x + 25 y ≤ 200

  2x + 9y ≤ 16

• x + y ≥ 200

  9x + 25y ≤ 16

• 9x + 25y ≥ 200

  x + y ≤ 16

• 7 candy bars &

  3 shirts

• 9 candy bars &

  1 shirt

• 5 candy bars &

  1 shirt

• 1 candy bar &

  10 shirts

• 4 candy bars &

  4 shirts

A company produces two products, Product A and Product B. The profit per unit of Product A is $5 and the profit per unit of Product B is $8. The company wants to maximize its profit while producing at least 100 units of Product A and at least 80 units of Product B. Write a system of linear inequalities to represent this situation.

• 5x + 8y ≥ 0, x ≥ 100, y ≥ 80

• 5x + 8y ≥ 0, x ≤ 100, y ≤ 80.

• 5x + 8y ≤ 0, x ≥ 100, y ≥ 80.

• 5x + 8y ≥ 0, x ≥ 50, y ≥ 80.

Since Lexie can’t make a negative number of cobblers or pies, what additional constraints exist on our variables? Select all that apply.

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

• 32

• 16

• 27

• 45

The members of a new band want to spend no more than $75 for at least 60 fliers to advertise their upcoming concert. The cost color fliers is $1.50 each, the cost of black and white fliers is $0.75 each. Which of the following combinations is a reasonable solution?

• 26 color, 30 black and white

• 30 color, 35 black and white

• 60 color

• 30 color, 50 black and white

Luka and Dana are making cookies for the Westland Pantry. They only have up to 8 hours to bake! They can bake 32 chocolate chip cookies in an hour (x), and 20 snickerdoodle cookies in an hour (y). They need to make at least 150 cookies. Which region represents more than 150 cookies made?

• Red

• Blue

• Purple (overlap of red and blue)

• Non- Shaded

A handicraft factory produces x units of hats and y units of baskets everyday. The number of hats produced is not more than 50 units per day. The total production is at least 150 units a day. The number of baskets is not more than two times the number of hats produced.

Mr. Shah is ordering chicken wings and fries for his son’s birthday party and has a budget of $81. An order of a bucket of chicken wings costs $13 and an order of basket of fries costs $7. Inequality: 13x+7y≤81 b) Graph in Desmos!! c) Choose all possible solutions below:

• 3 buckets of chicken wings & 2 baskets of fries

• 5 buckets of chicken wings &

  1 basket of fries

• 10 buckets of chicken wings &

  0 baskets of fries

• 0 buckets of chicken wings &

  10 baskets of fries

• 5 buckets of chicken wings &

  5 baskets of fries