Question

Write a linear cost function for the situation. Identify all variables used. A parking garage charges 4 dollars plus 65 cents per half-hour. A linear cost function for the situation is C(x)=L (Use integers or decimals for any numbers in the expression)

Answer 1

The linear cost function is
`C(x)=1.3x+4` dollar.

Explanation:

Given : A parking garage charges 4 dollars plus 65 cents per half-hour. A linear cost function for the situation is C(x)=L.

To find : Write a linear cost function for the situation ?

Solution :

Cost function is defined as sum of marginal cost and fixed cost.

Let x be the number of hours i.e. time for which parking cost.

A parking garage charges 4 dollars plus 65 cents per half-hour.

The fixed price is $4.

Marginal cost is 65 cents per half-hour.

Converting cents into dollar,

1 cent = 0.01 dollar

65 cent = 0.65 dollar

The cost of
`(1)/(2)` hour = $0.65

The cost of x hours =
`0.65* 2x`

So, marginal cost is $1.3x.

Cost function is defined as

`C(x)=MC+FC`

`C(x)=1.3x+4`

`C(x)=1.3x+4` dollar.

Therefore, The linear cost function is
`C(x)=1.3x+4` dollar where x is the number of hours.