The costs of doing business for a company can be found by adding fixed costs, such as rent, insurance, and wages, and variable costs, which are the costs to purchase the product you are selling. The portion of the company’s fixed costs allotted to this product is $195, and the supplier’s cost for a set of tile is $5 each. Let x represent the number of tile sets.

Question

The costs of doing business for a company can be found by adding fixed costs, such as rent, insurance, and wages, and variable costs, which are the costs to purchase the product you are selling. The portion of the company’s fixed costs allotted to this product is $195, and the supplier’s cost for a set of tile is $5 each. Let x represent the number of tile sets.

Suppose the revenue equation is R = -x^2+62x

Can anyone help walk me through this, thanks.

Answer 1

R = -x^2 + 62x.

-x^2 + 62x = 0,
-x(x-62) = 0,
-x = 0,
x = 0.

x-62 = 0,
x = 62 sets.

C = $5x + $195,
C = 5*62 + 195 = $505.

Answer 2

Graph the function. Find the vertex, line of symmetry and maximum value.

f(x)=(x+3)^2-2

Answer 3

Sure! I can help you understand this problem step by step.

To start, let's break down the given information:

1. Fixed costs: Fixed costs are costs that do not change with the number of units produced or sold. In this case, the portion of fixed costs allocated to the product is $195.

2. Variable costs: Variable costs are costs that vary depending on the number of units produced or sold. In this case, the supplier's cost for a set of tile is $5 each.

Now, let's move on to the revenue equation:

R = -x^2 + 62x

In this equation, R represents the revenue generated by selling the tiles, and x represents the number of tile sets sold.

The equation is in the form of a quadratic function. The quadratic term -x^2 indicates that the revenue is decreasing as the number of tile sets increases, while the linear term 62x indicates that the revenue increases as the number of tile sets increases.

Now, let's combine the information about costs and revenue to answer the question.

Total Cost (TC) = Fixed Costs + Variable Costs

Fixed Costs: The fixed costs for the product are given as $195.

Variable Costs: The variable costs depend on the number of tile sets sold. Since the supplier's cost for a set of tile is $5 each, the variable cost for x tile sets would be 5x.

So, the total cost equation would be:

TC = $195 + 5x

Now, to find the breakeven point, we need to find the value of x for which the revenue (R) and total cost (TC) are equal.

R = TC

So, we can equate the revenue equation and the total cost equation:

-x^2 + 62x = $195 + 5x

Simplifying this equation, we get:

-x^2 + 57x - $195 = 0

To solve this quadratic equation, you can use various methods like factoring, completing the square, or the quadratic formula.

Once you calculate the roots of the quadratic equation, those values of x will represent the number of tile sets needed to break even, where the revenue generated equals the total cost incurred.

I hope this explanation helps you understand the problem better! Let me know if you have any further questions.