Equations, systems of equations and linear inequalities in two variables
Equations, systems of equations and linear inequalities in two variables
Instructions:
IV.
Determine the breakeven point in the following problems.
Solve exercises about equations, systems of equations and linear inequalities in two
variables. You must present the procedure for each exercise.
1. The fixed costs for producing a certain item are $ 4403 per month and the
Exercises:
variable costs are $ 4.50 per unit. If the producer sells each of the items for $
8, determine and explain the balance point.
I. Solve the following systems of linear equations using the substitution method.
2. The cost to produce "x" items is given by ye = 2.8x + 1617, where yc is the
1. 1_2xty = 3
total cost to produce "x" items. Each "x" item produced sells for $ 7.
a. Find the point of balance.
3x + 2y = 12
b. If it is known that at least 175 units will be sold, what should be the
2. -4x + 3y = -16
price set for each item to ensure there are no losses?
3.
[3x + 2y = 12
3. The cost of producing "x" items per month is given by C (x) = $ 1,800 + $ 6x If
19x + 6y = 24
each item can be sold for $ 9,
a. Determine the breakeven point.
II. Solve the following systems of linear equations using the elimination method.
b. If the manufacturer can reduce variable costs to $ 4 per item by
3x + 2y = 6
increasing fixed costs to $ 2,425 a week, will it be convenient to do so?
1. 5x + 9y = -24
2.
(-4x - 3y = -16
8x + 6y = 32
( x + 3y = 12
3. 4x - 3y = 18
III.
Solve the following systems of linear inequalities using the graphic method.
1.
3x + 2y < -6
15x - 3y < 12
4x + 3y 29
2. -5x + 7y <-7