The linear function is well-known in business economics. It is attrenergetic because it is straightforward and also simple to handle mathematically. It has actually many type of crucial applications.
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Liclose to attributes are those whose graph is a directly line.
A straight function has actually the complying with form
y = f(x) = a + bx
A direct attribute has one independent variable and one dependent variable. The independent variable is x and the dependent variable is y.
a is the continuous term or the y intercept. It is the value of the dependent variable once x = 0.
b is the coeffective of the independent variable. It is additionally well-known as the slope and also provides the rate of readjust of the dependent variable.
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To graph a straight function:
1. Find 2 points which meet the equation
2. Plot them
3. Connect the points through a directly line
Example:
y = 25 + 5x
let x = 1 then y = 25 + 5(1) = 30
let x = 3 then y = 25 + 5(3) = 40
A easy instance of a direct equation
A firm has actually solved prices of $7,000 for plant and equuipment and also variable costs of $600 for each unit of output. What is complete price at varying levels of output?
let x = units of output let C = total cost
C = addressed price plus variable price = 7,000 + 600 x
| output | total cost |
| 15 systems | C = 7,000 + 15(600) = 16,000 |
| 30 systems | C = 7,000 + 30(600) = 25,000 |
Combinations of straight equations
Liclose to equations deserve to be included together, multiplied or separated.
A easy example of addition of linear equations
C(x) is a price function
C(x) = addressed price + variable cost
R(x) is a revenue function
R(x) = selling price (number of items sold)
profit amounts to revenue much less cost
P(x) is a profit function
P(x) = R(x) - C(x)
x = the number of items developed and sold
Data:
A agency receives $45 for each unit of output marketed. It has a variable price of $25 per item and a addressed expense of $1600. What is its profit if it sells (a) 75 items, (b)150 items, and (c) 200 items?
| R(x) = 45x | C(x) = 1600 + 25x |
| P(x) = 45x -(1600 + 25x) | |
| = 20x - 1600 |
| let x = 75 | P(75) = 20(75) - 1600 = -100 a loss |
| let x = 150 | P(150) = 20(150) - 1600 = 1400 |
| let x = 200 | P(200) = 20(200) - 1600 = 2400 |