Linear Inequalities in Two Variables and Linear Programming

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

• 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

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.

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

• 300

• 280

• 400

• 240

Kelly can work for her dad and make $6.00 per hour, or she can work for Jana's Mowing Service and make $14.00 per hour. She needs to make at least $84, and can only work 10 hours total. Write a system of equations to represent this scenario.

A student with two summer jobs earns $11 per hour at a coffee shop and $15 per hour at retail store  The student would like to earn at least $800 per month.  Select all the possible combinations the student can work.

• 80 hours at coffee shop and 40 hours at retail store

• 40 hours at coffee shop and 20 hours at retail store

• 20 hours at coffee shop and 60 hours at retail store

• 20 hours at coffee shop and 20 hours at retail store

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

Mr. Newman's class needs to sell at least 70 tickets for the school's car wash for them to raise money for their class t-shirt. Morning tickets cost $4 and afternoon tickets cost $6. If their goal is to raise more than $450, which system of inequalities can be used to determine the number of morning tickets, m, and afternoon tickets, a, they need to sell?