Knowee
Questions
Features
Study Tools

Assume it costs Microsoft $4,300 to manufacture 6 Xbox 360s and $7,900 to manufacture 12. Obtain the corresponding linear cost function.C(x) = What was the cost (in dollars) to manufacture each additional Xbox?$ Use the cost function to estimate the cost of manufacturing 60 Xboxes (in dollars).$

Question

Assume it costs Microsoft 4,300tomanufacture6Xbox360sand4,300 to manufacture 6 Xbox 360s and 7,900 to manufacture 12. Obtain the corresponding linear cost function.C(x) = What was the cost (in dollars) to manufacture each additional Xbox?Usethecostfunctiontoestimatethecostofmanufacturing60Xboxes(indollars). Use the cost function to estimate the cost of manufacturing 60 Xboxes (in dollars).

🧐 Not the exact question you are looking for?Go ask a question

Solution

To find the cost function, we first need to determine the slope of the line that connects the two points given. The slope (m) is given by the formula:

m = (y2 - y1) / (x2 - x1)

Here, our two points are (6, 4300) and (12, 7900). So, we substitute these values into the formula:

m = (7900 - 4300) / (12 - 6) = 3600 / 6 = 600

This means that the cost to manufacture each additional Xbox is $600.

The cost function of a line is given by the formula:

C(x) = mx + b

We already know that m is 600. To find b (the y-intercept), we can substitute one of our points into the equation. Let's use (6, 4300):

4300 = 600*6 + b 4300 = 3600 + b b = 4300 - 3600 = 700

So, the cost function is:

C(x) = 600x + 700

To find the cost of manufacturing 60 Xboxes, we substitute x = 60 into the cost function:

C(60) = 600*60 + 700 = $37,000.

This problem has been solved

Similar Questions

A manufacturer of DVD players has weekly fixed costs of $1,520 and variable costs of $12.50 per units for one particular model. The company sells this model to dealers for $19.50 each.Match the statement with the correct answer.Write the function for the weekly total costs, C(x). Write the function for the total revenue function, R(x). Write the function for the profit function, P(x). This is the cost (in dollars) of producing 150 DVD players. This is the profit (in dollars) when 150 DVD players are sold but since it is negative it means that the company loses money when 150 DVD players are sold. Each additional DVD player sold increases the profit by this many dollars. This is the revenue (in dollars) generated from the sale of 150 DVD players.

A manufacturer of soccer balls has a monthly fixed cost of $300 and a processing cost of $19 for each soccer ball produced. If x represents the number of soccer balls produced/sold, determine the total cost function, C(x).

You are ordering shirts for a club at your school. The function f(x)=12x+25𝑓(𝑥)=12𝑥+25 represents the cost of ordered x𝑥 shirts. How much would it cost to buy 6868 shirts? It cost $$ Answer 1 Question 19 to buy 6868 shirts.

Suppose you are the owner of a dairy company that produces milk powder. There is a fixed cost 6.4 thousand dollars every month and variable cost 9.41 thousand dollars per ton of milk powder. Write down the monthly total cost function (dollars in thousands) in the quantity of production Q (in tonnes). What is the slope of this linear function? Question 2 Answer a. none of the others b. -0.68 c. 6.4 d. 8.10 e. 9.41

The manager of a furniture factory finds that it costs $2400 to manufacture 100 chairs in one day and $4800 to produce 300 chairs in one day.(a) Express the cost C (in dollars) as a function of the number of chairs x produced, assuming that it is linear.C = Sketch the graph. (b) What is the slope of the graph?What does it represent?It represents the time (in days) to produce each additional chair.It represents the number of chairs produced.    It represents the cost (in dollars) of operating the factory daily.It represents the cost (in dollars) of producing each additional chair.(c) What is the y-intercept of the graph?What does it represent?It represents the time (in days) to produce each additional chair.It represents the number of chairs produced.    It represents the cost (in dollars) of producing each additional chair.It represents the fixed daily cost (in dollars) of operating the factory.

1/3

Upgrade your grade with Knowee

Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.