The manager of a large apartment complex has found that the profit (in thousands of dollars) is given by P (x) = –2x² + 500x – 30000, where x is the - number of units rented. Answer the following questions: (i) What is the profit when 120 units are rented? (ii) How many units must be rented to earn a profit of $800,000? (iii) How many units should be rented to produce the maximum profit? (iv) What is the maximum profit?

Q: If Q(x) = x³ – 25x + 100 is the cost per item of producing x-items. Is the cost per item increasing…

A: Differentiate Q(x) w.r.t x to find the derivative for the function Q(x). The slope for function at…

Q: r believes that the profit P, in dollars, from selling x tickets is given by  P(x)= 35x − 0.25x2.…

A: Given P(x) = 35x - 0.25x2 → 1For maximum profit put P'(x) = 0⇒ P'(x) = 35 - 0.25(2x)⇒ P'(x) = 35 -…

Q: The manager of a small company that produces roof tile has determined that the total cost in​…

A: Consider the total cost C(x) in $ and the revenue cost R(x) in $. At BEP, the total cost function…

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

A:

Q: A tour operator believes that the profit P, in dollars, from selling x tickets is given by P(x)= 30x…

A:

Q: The total cost of producing a type of boat is given by C(x) = 17000 – 20x + 0.02x², where x is the…

A: Given:- The total cost of producing a type of boat is given by C(x) = 17000 - 20x + 0.02x2 where x…

Q: The management of the producers of a famous hot sauce estimate that their profit (in dollars) from…

A: We can use the concept of maxima and minima to solve this question.  In order to get maximum profit…

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 fast-food restaurant has a cost of production C(x)=12x+90 and a revenue function R(x)=7x. When…

A: Given,        C(x)=12x+90 and R(x)=7x

Q: The total costs for a company are given by C(x) = 4000 + 50x + x² and the total revenues are given…

A: Concept - Break-even point is a point at which revenue becomes equal to the cost.Given cost - C(x) =…

Q: The profit function,in dollars, for a product is given by  Π(x) = −x^3 + 76x^2 − 380x − 2800, where…

A: (a) Consider the provided profit function,

Q: 4) Suppose the cost of producing x items is given by C(x) 4000 - x3 and the revenue made on the sale…

A: Consider the given question,The breakeven point occurs where profit is zero or when revenue equal to…

Q: The profit P (in dollars) generated by selling x units of a certain commodity is given by P( x) =…

A:

Q: The weekly revenue from the production and sale of x units of grain is given by R(x) = 237x - x…

A: The weekly revenue from the production and sale of x units of grain is given by- R(x)=237x-x2 The…

Q: If a company has total costs C(x)=45,000+35x+.3x2 and the total revenues given by R(x)=625x-.7x2,…

A: The given cost function is C(x)=45,000+35x+.3x2. The given total revenue function is R(x)=625x-.7x2.…

Q: The management of the producers of a famous hot sauce estimate that their profit (in dollars) from…

A:

Q: A jewelry maker incurs costs for a necklace according to C(X) = 37x + 1650. If the revenue function…

A: Given that  C(X) = 37x + 1650. R(x) = 87x

Q: The total amount spent by some number of people on clothing and footwear in the years​ 2000-2009 can…

A: The solution is given below :

Q: An appliance company determined that in order to sell X dishwashers, the price per dishwasher must…

A:

Q: A catering company estimates that, if it has x customers in a typical week, its expenses will be…

A: Given: C(x) = 550x + 6500  R(x) = 1200x (a) How much profit will the company earn in 1 week when it…

Q: Why does the graphy of the quadratic function f(x)=x2+4x+5 cross the y-axis but not the x-axis?

A: The graph the quadratic function crosses y axis because we can put x is equal to zero and get y…

Q: A tour operator believes that the profit P, in dollars, from selling x tickets is given by  P(x)=…

A: First of all, consider the given function P (x) which shows relation between the profit of a tour…

Q: A tour operator believes that the profit P, in dollars, from selling x tickets is given by P(x) =…

A:

Q: (b) Show that ifr (x) = 6x and c (r) = x³ – 6x² +15x are your revenue and cost functions, then the…

A:

Q: A soft-drink vendor at a popular beach analyzes his sales records and find that if he sells "x" Cans…

A:

Q: The total costs for a company are given by C(x) = 2000 + 40x + x^2 and total revenues are given by…

A:

Q: A fast-food restaurant has a cost of production C (x) = 13x + 126 and a revenue function R(x) = 6x.…

A: Given: C(x)=13x+126 R(x)=6x The company will start to turn a profit when the revenue function will…

Q: The net profit in dollars per day for a small business owner is given by the equation f (x) = -0.1x²…

A:

Q: A laptop company has discovered their daily cost and revenue functions:  C (x) = 3x2 − 10x + 200…

A: The cost function is, C(x)=3x2−10x+200 The revenue function is, R(x)=−2x2+100x+50

Q: The management of the producers of a famous hot sauce estimate that their profit (in dollars) from…

A: The management of the producers of a famous hot sauce estimate that their profit (in dollars) from…

Q: Solve the initial condition problem: f"(x) = 60x³ + 24x², f(2) = 239, f(-3) = 254

A: f''x=60x3+24x2 take integration  ∫ f''x=∫ 60x3+24x2dx f'x=∫60x3dx+∫ 24x2dx f'x=60x44+24x33+C…

Q: 2. Suppose the revenue R in thousands of dollars that a company receives from producing x thousand…

A: The problem involves the revenue function and its graph (a parabola). Note that the units x and R(x)…

Q: Callaway Golf Company has determined that the marginal cost C of manufacturing x Big Bertha golf…

A: The marginal cost C of manufacturing x is given by the equationC(x)=4.9x2-617.4x+19600

Q: The owner of a video store has determined that the profits P of the store are approximately given by…

A: Solve for the maximum profit

Q: A tour operator believes that the profit P, in dollars, from selling x tickets is given b

A: Given relation - P(x) = 50x-0.25x2where,P(x) = Profitx = number of ticketsDifferentiating P(x) with…

Q: A tour operator believes that the profit P, in dollars, from selling x tickets is given by P(x) =…

A: Given relation:P(x)=50x-0.25x2Where,P(x)=Profitx-number of tickets Differentiate P(x) with respect…

Q: The total cost, in dollars, to produce bins of cat food is given by C(x)=15x+10582 The revenue…

A: The total cost, in dollars, to produce bins of cat food is given by C(x)=15x+10582 The revenue…

Q: A firm can produce only 2900 units per month. The monthly total cost is given by  C(x) = 500 + 200x…

A: Since, A firm can produce only 2900 units per month. where, the monthly total cost is given by  C(x)…

Q: Suppose a baby food company has determined that its total revenue R for its food is given by R = - x…

A: R=-x3+45x2+525x To find: Production level that will yield maximum revenue.

Q: 3.) The revenue for a company producing widgets is given by 25x - 50x + 200, where x is the price in…

A:

Q: A duck dives under water and its path is described by the quadratic function y=2x-4x, where y…

A: y=2x2-4x The position of duck to dive down 2 meters y=-2 -2=2x2-4x 2x2-4x+2=0 2(x2-2x+1)=0…

Q: If the profit function for a product is  P(x) = 1200x + 80x2 − x3 − 58,000  dollars, selling how…

A: P(x)=1200x+ 80x2 -x3…

Q: The total revenue​ (in hundreds of​ dollars) from the sale of x spas and y solar heaters is…

A:

Q: 4) The number of mosquitoes M(x), in millions, in a certain area depends on the June rainfall x, in…

A: Maximum number of mosquitoes

Q: The total profit (in tens of dollars) from the sale of x hundred boxes of candy is given by P ( x )…

A:

Q: Suppose the revenue R in thousands of dollars that a company receives from producing x thousand…

A:

Q: (b) Show that if r (x) = 6x and c (x) = x – 6x² +15x are your revenue and cost functions, then the…

A: Answer for 2(b) b) Show that if r(x)=6x and c(x)=x3-6x2+15x are revenue and cost functions, then we…

Q: A tour operator believes that the profit P, in dollars, from selling x tickets is given by P(x) =…

A: A tour operator believes that the profit P, in dollars, from selling x tickets is given by P(x) =…

Q: Find the number of units that must be sold to break even.

A: