A firm produces a commodity and receives $100 for each unit sold. The cost of producing and selling x units is 20x + 0.25x² dollars. Find the number of units the company should produce in order to maximize profit, and find the maximum profit.

Q: Complete the square and find the minimum or maximum value of the quadratic function. y = 2x 2 - 4x -…

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Q: Two sisters decide to set up a hotdog stand. The profit they make from the stand can be modeled by…

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Q: Find the value of x for which y = x5 – 5x3 – 20x – 2 will have a maximum point.

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Q: What is the maximum number of times that a quadratic function can intersect the x-axis?

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Q: . The Minimum point of y = x3 3x+6

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Q: An artist can sell 20 copies of a painting at $100 each, but for each additional copy she makes, the…

A: SOLUTION-

Q: A firm can produce only 3200 units per month. The monthly total cost is given by C(x) = 500 + 200x…

A: The total cost function is given as  And the revenue function is given as Then the profit function…

Q: Find the Maximum height of h(x) = -4x^2 + 320x + 100.

A: The given height function is h(x)=-4x2+320x+100

Q: A soft-drink vendor at a popular beach analyzes their sales records and finds that if they sell x…

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Q: The monthly profit from the sale of x units of a product is P = 80x-0.042-12000 dollars. (a) What…

A: Here is the solution of the given problem. Maximum Profit Function.

Q: A company makes a profit of $50 per software program and $35 per video game. The company can produce…

A: We will solve the given equation as shown below by using graph tool

Q: Find the value or values of x for which y = 8x3 - 9x2 + 1 has a maximum or minimum value.

A: Given: y=8x3-9x2+1

Q: Find the vertex of the graph of the quadratic function and determine whether it's an absolute…

A: Given y=x2+18x+83 Find Vertex of the graph and determine whether it's an absolute maximum or…

Q: The revenue of a charter bus company depends on the number of unsold seats. If the revenue R(x) is…

A: Given: The revenue of a charter bus company is,  Rx=8000+70x-x2. Here, x is the number of unsold…

Q: A company manufactures and sells x cellphones per week. The weekly​ price-demand and cost equations…

A: Weekly price demand is P(x)=400 - 0.5x cost equation C(x) = 15000+135x

Q: A company manufactures and sells x cellphones per week. The weekly​ price-demand and cost equations…

A: This question is related to price and cost functions, we will solve it using given information.

Q: If the profit function for a product is P(x) = 6400x + 80x² – x³ – 190,000 dollars, selling how many…

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Q: A fitness club charges a $50 membership price per month. At this price, the club can attract 504…

A: Suppose p be the price and x be the number of member's. The Px,p=504,50 and Qx,p=528,48 Now use the…

Q: Determine the break-even quantities (Minimum and Maximum Quantities). R(x)= -2x2+20x, C(x)= 4x-40

A: Break even occurs when C(x)=R(x)

Q: Give the domain and range of the quadratic function whose graph is described.   Maximum equals=- 3…

A: A quadratic function is of the form: This is a degree 2 polynomial Polynomials exist for all real…

Q: If the revenue function is           R=500x-2x2  a)  Find the vertex .  b) What is the maximum…

A: Given revenue function is                                                              R=500x-2x2…

Q: Complete the square and find the minimum or maximum value of the quadratic function. y = −9x2 + x

A: A parabola with equation of the form y=a(x-h)2+k has vertex at (h,k) and opens up or down. If it…

Q: The Minimum point of y = 8x+4 (x-2)²

A: Use a graphing utility to plot the function. Use the utility to determine the minimum point.

Q: If the profit function for a product is P(x) = 5600x + 65x2 − x3 − 122,000 dollars, selling how…

A: The given profit function is: P(x)=-x3+65x2+5600x-122000

Q: Find the maximum point, minimum point, and inflection point 1. y = x³ - 3x? + 8

A: Given query is to find maximum, minimum and inflection point.

Q: A company can produce a maximum of 25 widgets in a day. If they sell x widgets during the day then…

A: Above question is solved.

Q: Given f(x) = 7x2-4x-2, without graphing, determine whether it has a maximum value or minimum value,…

A: Given function is f(x) = 7x2-4x-2 1. Find f'(x)    f'(x)=14x-4 2. Finding the critical point by…

Q: Without graphing, determine whether the given quadratic function, f(x) = -x² +2x- 5, has a maximum…

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Q: Video Productions produces DVDs selling for $20 per unit. Fixed costs are $40,000 and the…

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Q: the profit function for a product is P(x) = 1800x + 75x2 − x3 − 54,000 dollars, selling how many…

A: GivenP(x) = 1800x + 75x2 - x3 - 54,000To find number of items that miximize the profit

Q: What is the maximum number of real solutions a system of equations composed of a linear function and…

A: Quadratic function has a degree 2 and linear function has a degree 1.

Q: An editor has been allotted $60,000 to spend on the development and promotion of a new book. It is…

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Q: Determine whether h(x) = -6x² + 7x + 3 has a minimum value or a maximum value, and then find the…

A: Consider the equation  h(x)=−6x2+7x+3

Q: The annual total revenue for a product is given by R(x) = 10,000x – 5x2 dollars, where x is the…

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Q: The product of two numbers is 24. Find the numbers if (a) the sum of the two numbers is minimum, (b)…

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Q: The Maximum point of y = 9-x² x²-4

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Q: a rancher has 720 feet of fencing to construct six corrals, find the dimensions that maximized the…

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Q: An international organization must decide how to spend the $2,200,000 they have been allotted for…

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Q: An airline finds that if it prices a cross-country ticket at $400, it will sell 500 tickets per day.…

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Q: If the profit function for a product is  P(x) = 3000x + 65x2 − x3 − 76,000  dollars, selling how…

A: Solve the following

Q: If the profit function for a product is P(x) = 3500x + 80x² – x³ – 108,000 dollars, selling how many…

A: given,        Px=3500x+80x2-x3-108000

Q: Find the maximum value of the quadratic function.  f(x)= - 3x2 + x - 7

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Q: 3. The total profit (in thousands of dollars) from the sale ofx hundred thousand automobile tires is…

A: Explanation of the answer is as follows

Q: The profit of a cell phone manufacturer is found by the function y= -2x2+108x+75, where x is the…

A: Solution of question as follows

Q: airline finds that if it prices a cross-country ticket at $300, it will sell tickets per day. It…

A: Let 'x' be the number of $20 price reduction and the number of 40 tickets more sold per day. Let…

Q: If the profit function for a product is  P(x) = 4200x + 55x2 − x3 − 88,000  dollars, selling how…

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Q: Lynbrook West, an apartment complex, has 100 two-bedroom units. The monthly profits (in dollars)…

A: For maximum profit we will have dP/dx=0 From there solve for x. x=88

Q: The daily profit, P dollars, of a ice cream vendor is mode-led by the equation P = -60(x-3)2+ 140,…

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Q: The profit for a product is given by P = 1600 – 100x + x² , where x is the number of units produced…

A: P = 1600-100x +x2a) for minimum profit dPdx =0dPdx= -100+2x = 0        dPdx<0 till   x = 50⇒x =…

Q: What is the optimal value of the quadratic relation y = - 5 x^2 + 10?

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.