A small fast food restaurant invests $4000 to produce a new food item that will sell for $3.50. Each item can be produced for $2.15. Which of the following systems shows the cost and revenue functions for x items produced and sold?
cost = 4000 + 2.15 x
rev = 3.50 x
To determine the cost and revenue functions for the small fast food restaurant, we need to understand the concepts of cost and revenue.
Cost Function:
The cost function represents the total cost incurred in producing a certain number of items. In this case, the cost function will be determined by the fixed cost of $4000 invested in producing the new food item, as well as the variable cost per item.
Let's denote the number of items produced and sold as "x".
The fixed cost is $4000, which remains constant regardless of the number of items produced and sold.
The variable cost per item is $2.15, which means it will vary depending on the number of items produced and sold. Therefore, the variable cost for 'x' items can be represented as: 2.15x.
To find the cost function, we can combine the fixed and variable costs:
Cost Function: C(x) = 4000 + 2.15x
Revenue Function:
The revenue function represents the total revenue generated from selling a certain number of items. In this case, the revenue function can be calculated by multiplying the price of each item by the quantity sold.
The price per item is $3.50, and the quantity sold is 'x'. Therefore, the revenue function can be represented as: 3.50x.
Revenue Function: R(x) = 3.50x
Now that we have derived the cost and revenue functions, here is the summary:
Cost Function: C(x) = 4000 + 2.15x
Revenue Function: R(x) = 3.50x