Cost, Revenue, and Profit A company invests $98,000 for equipment to produce a new product. Each unit of the product costs $12.20 and is sold for $16.98. Let x be the number of units produced and sold. (a) Write the total cost C as a function of x. C(x) = 98000+16.98x (b) Write the revenue R as a function of x. R(x) = 207.156 (c) Write the profit P as a function of x. P(x) = 4.78

Given:

Investment on equipment = $98,000

Cost of each unit = $12.20

Selling price of each unit = $16.98.

To find:

(a) The total cost C as a function of x.

(b) The revenue R as a function of x.

(c) The profit P as a function of x.

Solution:

Let x be the number of units produced and sold.

We have,

Fixed cost = $98,000

Variable cost = $12.20x

Total cost = Fixed cost + Variable cost

Therefore, the cost function is .

Selling price of each unit = Revenue from each unit =  $16.98.

Total revenue = Revenue from x units

Therefore, the revenue function is .

Profit = Revenue - Cost

Therefore, the profit function is .

first option

a function is a relation in which an input is paired with exactly one output.

so, let's find the right answer.

in our first option, our inputs are january, february, and march. the outputs are 30, 28, and 25. each input has it's own output. this is correct!

our second option we know is incorrect, because ms. valverade has two outputs, dogs and cats. this is not a function.

our third option is incorrect as well. the yellow square has two ouputs, the square and the triangle.

lastly, in our fourth option, we see the number 7 two times with a different output. therefore, this is not a function.

remember: each input must be paired with only one output!

because linear equations are a lot simpler than quadratics equations, and linear equations formula is a lot easier to memorize. that's why i think they're harder.