Question

A company determines its total revenue and total cost functions for producing and selling x items...

A company determines its total revenue and total cost functions for producing and selling x items are given by

R(x)=600x−2x2, andC(x)=200+10x.

If the company produces and sells 2 additional items every day (in other words, dxdt=2), what is the rate of change of profit with respect to time when they've produced and sold 10 items?

Math   Calculus   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

Note: sinc profit = revenue-cost.

So using the given information we calculate profit function and then differentiate with respect to t.

Details explained in the image.

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
For a certain company, the cost for producing x items is 50x+300 and the revenue for...
For a certain company, the cost for producing x items is 50x+300 and the revenue for selling x items is 90x−0.5x2. The profit that the company makes is how much it takes in (revenue) minus how much it spends (cost). In economic models, one typically assumes that a company wants to maximize its profit, or at least wants to make a profit! Part a: Set up an expression for the profit from producing and selling x items. We assume that...
For a certain company, the cost for producing x items is 50x+300 and the revenue for...
For a certain company, the cost for producing x items is 50x+300 and the revenue for selling x items is 90x−0.5x2. The profit that the company makes is how much it takes in (revenue) minus how much it spends (cost). In economic models, one typically assumes that a company wants to maximize its profit, or at least wants to make a profit! Part a: Set up an expression for the profit from producing and selling x items. We assume that...
For a certain company, the cost for producing x items is 50x+300 and the revenue for...
For a certain company, the cost for producing x items is 50x+300 and the revenue for selling x items is 90x−0.5x2. The profit that the company makes is how much it takes in (revenue) minus how much it spends (cost). In economic models, one typically assumes that a company wants to maximize its profit, or at least wants to make a profit! Part a: Set up an expression for the profit from producing and selling x items. We assume that...
For a certain company, the cost of producing x items is 55x+300 and the revenue for...
For a certain company, the cost of producing x items is 55x+300 and the revenue for selling x items is 95x-0.5^2. Part A: Set up an expression for the profit from producing and selling x items. Part B: Find two values of x that will create a profit $300. Part C: Is it possible for the company to make a profit of $15000?
A firm produces two products A and B. The total cost function of producing “x” items...
A firm produces two products A and B. The total cost function of producing “x” items of product A and “y” items of product B is TC = 2x2 + y2 – xy – 49x + 425. Find the number of each type that should be produced to minimize the total cost if the firm is committed the producing 21 items in total.
A company has determined that its weekly total cost and total revenue (in dollars) for a...
A company has determined that its weekly total cost and total revenue (in dollars) for a product can be modeled by C(x) = 4000 + 30x R(x) = 300x -0.001x^2, where x is the number of items produced and sold. If the company can produce a maximum of 100,000 items per week, what production level will maximize profit?
The revenue and cost functions for a particular product are given below. The cost and revenue...
The revenue and cost functions for a particular product are given below. The cost and revenue are given in dollars, and x represents the number of units . R(x) = −0.2x2 + 146x C(x) = 66x + 7980 (a) How many items must be sold to maximize the revenue? (b) What is the maximum revenue? (c) Find the profit function. P(x) =   −.2x2+212x+7980 (d) How many items must be sold to maximize the profit? (e) What is the maximum profit?...
Given the revenue and cost functions R = 26x - 0.3x2 and C = 3x +...
Given the revenue and cost functions R = 26x - 0.3x2 and C = 3x + 10, where x is the daily production, find the rate of change of profit with respect to time when 20 units are produced and the rate of change of production is 7 units per day per day.
A company's revenue from selling x items is given by the function R(x)=44x and it's from...
A company's revenue from selling x items is given by the function R(x)=44x and it's from selling x items is given by the function C(x)=x2+384. Which of the following statements about their profitability is true? The company must sell at least 2 and at most 12 items to make a profit. The company must sell at least 5 and at most 20 items to make a profit. The company must sell at least 10 and at most 28 items to...
A furniture company determines that its marginal cost function for producing x tables is estimated by...
A furniture company determines that its marginal cost function for producing x tables is estimated by the function MC(x)=C(prime) of (x) = 0.6x^2 - 2.4x + 50 dollars per table. If the total cost of producing 25 tables is $1020. What is the total cost of producing 30 tables?
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT