Writing linear functions

Question

Assume that the cost to produce an item is a linear function and all items produced are sold. The fixed cost for the item is $2400, the variable cost per item is $120, and the item sells at $150. Write linear functions to model cost, revenue and profit.

Answer 1

for the cost:

 

cost = fixed cost + variable cost

 

the fixed cost does not change no matter how many items you produce... $2400 for this question.

 

the variable cost changes depending on how many items you produce.

 

for this one the variable cost is $120 per each item.

 

let's let x be the number of items we produce so the variable cost will be $120 times x

 

C = $2400 + $120x

 

 

Revenue:

 

That is how much money you make when you sell your product.

 

For this one you make $150 for each item you sell

 

remember that x is the number of items you sell.

 

R = $150x

 

 

Profit:

 

to get the profit you subtract your cost from the revenue (the amount you make when you sell them)

 

Profit = Revenue - Cost

 

P = $150x - ($2400 + $120x)

 

Let me know if you need me to explain any part of that better.

 

Kathy  :-)