Knowee
Questions
Features
Study Tools

The total cost (in dollars) for a company to manufacture and sell 𝑥 items per week is 𝐶=50⁢𝑥+2960, whereas the revenue brought in by selling all 𝑥 items is 𝑅=140⁢𝑥-0.6⁢𝑥2. How many items must be sold to obtain a weekly profit of $400?Hint: Profit = Revenue - Cost.They need to sell or items.

Question

The total cost (in dollars) for a company to manufacture and sell 𝑥 items per week is 𝐶=50⁢𝑥+2960, whereas the revenue brought in by selling all 𝑥 items is 𝑅=140⁢𝑥-0.6⁢𝑥2. How many items must be sold to obtain a weekly profit of $400?Hint: Profit = Revenue - Cost.They need to sell or items.

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

Solution

To find out how many items must be sold to obtain a weekly profit of 400,weneedtosettheprofitequation(Profit=RevenueCost)equalto400, we need to set the profit equation (Profit = Revenue - Cost) equal to 400 and solve for x.

Given: Cost, C = 50x + 2960 Revenue, R = 140x - 0.6x^2 Profit = R - C

We substitute the given equations into the profit equation:

Profit = (140x - 0.6x^2) - (50x + 2960)

Simplify the equation:

Profit = 90x - 0.6x^2 - 2960

We want to find the number of items (x) that will give a profit of $400, so we set the equation equal to 400 and solve for x:

400 = 90x - 0.6x^2 - 2960

Rearrange the equation:

0.6x^2 - 90x + 3360 = 0

This is a quadratic equation in the form ax^2 + bx + c = 0. We can solve for x using the quadratic formula x = [-b ± sqrt(b^2 - 4ac)] / 2a:

x = [90 ± sqrt((90)^2 - 40.63360)] / (2*0.6)

Solving this equation will give us the number of items that need to be sold to obtain a weekly profit of $400.

This problem has been solved

Similar Questions

A business has fixed costs of $3,570 per month and the product sells for $105. The variable cost is $26 per unit.The business wishes to make a profit of $4,227 AFTER tax.How many units must be sold? Answer in whole units only.

A cereal company estimates that its monthly cost is 𝐶(𝑥)=400𝑥2+300𝑥C(x)=400x 2 +300x and its monthly revenue is 𝑅(𝑥)=−0.6𝑥3+900𝑥2−400𝑥+700R(x)=−0.6x 3 +900x 2 −400x+700, where x is in thousands of boxes sold. The profit is the difference between the revenue and the cost.What is the profit function, P(x)?A.𝑃(𝑥)=0.6𝑥3−500𝑥2+700𝑥−700P(x)=0.6x 3 −500x 2 +700x−700B.𝑃(𝑥)=0.6𝑥3−1300𝑥2+100𝑥+700P(x)=0.6x 3 −1300x 2 +100x+700C.𝑃(𝑥)=−0.6𝑥3+1300𝑥2−100𝑥+700P(x)=−0.6x 3 +1300x 2 −100x+700D.𝑃(𝑥)=−0.6𝑥3+500𝑥2−700𝑥+700P(x)=−0.6x 3 +500x 2 −700x+700SUBMITarrow_backPREVIOUS

Our company sells a product for $120 per unit. Variable costs are $90 per unit and fixed costs are $4,000. The company expects to sell 200 units this year. How many units must we sell to earn a profit of $2,000?Group of answer choices200250300340

Dominic earns $285 per week plus an 8% commission rate on all his sales. If Dominic sells $4,213 worth of merchandise in one week, how much will his total earnings for the week be?

A business owner makes 50 items by hand in 40 hours. She could have earned $20 an hour working for someone else. Her total explicit costs are $200. If each item she makes sells for $15, her economic profit equals:

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.