Systems of Linear Inequalities Review
Answer the following questions. Show your work to get full marks. Please use Desmos whenever you are asked to graph any inequality or system of linear inequalities. Submit your work through Edmodo, or by email at XXXXXXXXXX.
1. State the inequality that is sketched in each of the following graphs. Make sure you include the domain and range in your answer.
a)
)
c)
d)
2. Malcolm and Skylar both work as
icklayers. Malcolm can lay 30
icks/hr and Skylar can lay 40
icks/hr. Together, they need to lay a minimum of 500
icks each working day.
a) Write an inequality that models the situation.
) Graph the inequality.
c) Give two different combinations of hours that satisfy the
inequality.
d) What real-life limitation comes into play in a question like this?
3. A sporting goods store orders hockey skates and gloves from the same supplier. Every week, they order at least 40 items. Skates cost the store $150 each and gloves cost $40 each. The store does not want to spend more than $4000/week.
a) Write out the system of linear inequalities that models this situation.
) Graph the system, including all key points.
c) Give at least two combinations of items that the store can buy.
4. Consider the following system of linear inequalities
What values of x and y maximize the objective function ?
5. A diet is to include at least 80 mg of Vitamin A and at least 100 mg of Vitamin B. These requirements can be met from two types of food. A tablespoon of food X has 1 mg of Vitamin A and 2 mg of Vitamin B. A tablespoon of food Y has 1 mg of Vitamin A and 1 mg of Vitamin B. The constraints of this problem can be represented by the following system of equations where x is the number of tablespoons of food X and y is the number of tablespoons of food Y:
A tablespoon of food X costs 36Â¢ and a tablespoon of food Y costs 30Â¢. How many tablespoons of each type of food should be purchased to satisfy the requirements at minimum cost?
Using this information, the objective function that describes the total cost of food is: . Find the solution that minimizes the objective function.
6. A farmer has a field of 60 acres in which he plants potatoes and turnip. The seed for potatoes costs $15 per acre, the seed for turnip costs $50 per acre and the farmer has set aside $2125 to spend on seed. The profit per acre of potatoes is $200 and the profit for turnip is $60 an acre. Find the number of acres of potato and turnip that needs to be planted to maximize the profit for the farmer.
2835
=+
Dxy
0
0
XXXXXXXXXXvitamin A)
XXXXXXXXXXvitamin B)
Â³
Â³
+Â³
+Â³
x
y
xy
xy
3630
=+
Cxy