2.5 - Linear Programming

​2.5 notes Linear Programming

By Rachel Jones

Fill in the Blanks

Imagine you are a baker, just starting out in the business. You make two things: donuts and pizzas. Unfortunately, your dough making machine can only make 100 balls of dough per hour. Each donut requires a single ball of dough but a pizza requires two balls of dough. If you made 10 donuts, what is the maximum number of pizzas you could make that hour?

You can make

balls of dough

Multiple Choice

You can make at most 70 donuts per hour due to physical restrictions.

If "x" represents the number of donuts produced per hour, which of the following statements is the best way of expressing this?

• $$x\le70$$

• $$70x\le60$$

• $$x<70$$

• $$x=70$$

• $$x\ge70$$

Math Response

Also, you can make at most 40 pizzas per hour. If y represents the number of pizzas produced per hour, write an inequality to represent this.

Type answer here

Correct Answer: y\le40

Deg^°

Rad

Multiple Select

By the way, you cannot make a negative number of donuts or pizzas. Using

"x" for the number of donuts produced each hour and

"y" for the number of pizzas for each hour,

choose the inequality/inequalities to represent this constraint.

• $$y\ge0$$

• $$y\ge x$$

• $$x\le60$$

• $$x\ge0$$

• $$y\le60$$

Multiple Choice

Your dough making machine can only make 100 balls of dough per hour.

Each donut requires a single ball of dough but a pizza requires two balls of dough.

Using `x` for the number of donuts produced each hour and `y` for the number of pizzas for each hour, choose the inequality to represent this constraint.

• $$x-2y\le100$$

• $$2x+y\le100$$

• $$y\ge2x+100$$

• $$x+y\le100$$

• $$x+2y\le100$$

Hotspot

Put points on the corners points (vertices) of the graph that represent the feasible region.

Multiple Choice

The bakery sells every donut or pizza that it makes. The profit made on each donut is $1.20 and the profit made on each pizza is $2.00. Which of the following is a rule for $"P", the total profit for making "x"

donuts and "y" pizzas in an hour?

• $$P=3.2xy$$

• $$P=1.2x+2y$$

• $$P=2x+1.2y$$

• $$P=x+y$$

• $$1.2P=2y$$

Labeling

Label each point with the appropriate points below.

Drag labels to their correct position on the image

(20,40)

(0,0)

(40,0)

(40,20)

(70,15)

(15,70)

(70,0)

(0,40)

(0,70)

Math Response

Recall that profit is $1.20 per donut and $2.00 per pizza. Calculate the profit at each corner point and hence work out the best combination of donuts and pizzas that should be made per hour. (you may need to use scratch paper to make a table)

Enter the maximum amount of profit made.

Type answer here

Correct Answer: 104

Deg^°

Rad

Fill in the Blanks

Recall that profit is $1.20 per donut and $2.00 per pizza. Calculate the profit at each corner point and hence work out the best combination of donuts and pizzas that should be made per hour. Enter the optimal number of donuts and pizzas, together with the total profit per hour.