Two carpet cleaning companies have different pricing structures. CarpetShine charges 1.80 AUD per square metre, plus an upfront scheduling fee of 50 AUD. CleanMaster has no scheduling a service fee, but the rate is 2.50 AUD per square metre. Let C1(x) and C2(x) be the costs, in AUD, of cleaning x square metres of carpet area by CarpetShine and CleanMaster respectively. (a) Write down expressions for the costs, C1 and C2, of cleaning x square metres of carpet [2] area. (b) Find the least number of whole square metres of carpet area cleaned by CarpetShine for its services to be a cheaper option. [3]

Q: If a company has total costs  C(x) = 10,000 + 55x + 0.1x2  and total revenues given by  R(x) =…

A: Profit = total Revenue - total cost          = R(x) - C(x)At break even point Profit = 0⇒ R(x) -…

Q: It has fixed costs of $2625 related to the production of the t-shirts, and the production cost per…

A: Hey, since there are multiple subparts posted, we will answer first 3 questions from iv to vi. If…

Q: If a company has total costs  C(x) = 16,000 + 35x + 0.3x2  and total revenues given by  R(x) =…

A:

Q: manufacturer of lighting fixtures has daily production costs of C = 800 - 30x + 0.75x^2, where C is…

A: Given query is to find the value of x for minimum cost.

Q: or a certain company, the cost function for producing x items is C(x)=40x+150 and the revenue…

A: Given,         For a certain company, the cost function for producing x items is Cx=40x+150…

Q: If the demand fuction for a good is p=110-x^2 and the supply function for it is…

A:

Q: manufacturer of color televisions can sell 2100 sets to his dealers at $⁢558 each. If the price is…

A:

Q: ood morning, may you help me please. Thank you If a company has total costs C(x) = 16,000 +…

A: Given that, Total cost C(x) = 16,000 + 25x + 0.2x2 Total Revenue R(x) = 305x − 0.8x2, We have to…

Q: Stuffco Industries makes model airplanes and wants to know their average cost and revenue at a…

A: Definition used-             Average cost -                          C-(x)=C(x)x           Average…

Q: Suppose that r(x) = 9x and c(x) = x3 - 6x2 + 15x are the revenue and the cost functions, given in…

A: Consider the given revenue function R and cost function C: Here the objective is to find the…

Q: Suppose it costs an appliance company $223 to manufacture each washer and $187 to manufacture each…

A: Given that cost of manufacturing for each washer is $223 and  cost of manufacturing for each dryers…

Q: The total costs for a company are given by C(x) = 5400 + 50x + x2 and the total revenues are given…

A: The break even point is the point where total cost equal to total revenues.

Q: If a company has total costs C(x)=24000+25x+0.1x^2 and total revenues given by R(x)=485x-0.9x^2,…

A:

Q: The total costs for a company are given by C(x) = 2700 + 90x + x2 and the total revenues are given…

A: The Break-even point occurs when total cost equals total revenue. So, we have to solve C(x)=R(x)

Q: If the Supply function for a product is given by p=200(2q), where q represents the number of units,…

A: The objective is to determined what will be the proce when the producers are willing to supply 500…

Q: The demand and supply functions for your college newspaper are, q = −9,000p + 4,000 and q = 2,000p +…

A:

Q: The cost and revenue functions for a certain firm are given by C(x) = 14x + 20,000 and R(x) = 22x,…

A:

Q: f in a monopoly market the demand for a product is p=1600-x and the revenue is R=px, where x is the…

A: Given,  The demand for a product is  p=1600-x Revenue is R = px  where x is the number of units sold…

Q: If the profit function for a firm is given by  P(x) = −1600 + 170x − x2  and limitations on space…

A: Here we have to find the break even point for given  profit function

Q: Stuffco Industries makes model airplanes and wants to know their average cost and revenue at a…

A:

Q: A manufacturing company that can produce from one up to forty per day, has estimated the following…

A:

Q: A company manufactures two types of bicycles, a racing bicycle and a mountain bicycle. The total…

A:

Q: If a company has total costs C(x) = 12,000 + 15x + 0.1x2 and total revenues given by R(x) = 275x -…

A: We have to solve

Q: If, in a monopoly market, the demand for a product is p = 160 − 0.10x and the revenue function is R…

A: Given,  The demand function :  p = 160-0.10x  The revenue function : R = px  Where x is the number…

Q: Suppose a calculator manufacturer has the total cost function C(x) =34x+6800 and the total revenue…

A:

Q: For producing a certain product, if total costs can be represented by C(x) = 1600 +1500x, and the…

A: Break even point is the point where the revenue function and the cost function is equal. Find the…

Q: The State of Maryland is considering a requirement that for every ton of CO2 produced by out-…

A:

Q: The total costs for a company are given by C(x) = 5400 + 20x + x2 and the total revenues are given…

A:

Q: If a company has total costs  C(x) = 45,000 + 35x + 0.1x2  and total revenues given by  R(x) =…

A:

Q: A manufacturer estimates that when x units of a particular commodity are sold domestically and y…

A: The profit function is given as: Px,y=x−3070+5x−4y+y−4080−6x+7yWhere x​​ units are sold…

Q: The cost and revenue functions for a certain firm are given by C(x) = 14x + 20,000 and R(x) = 22x,…

A: Given: C(x) = 14x + 20,000  and R(x) = 22x Profit function P(x) is given by : P(x)=R(x)-C(x)…

Q: If the profit function for a firm is given by P(x) = −5700 + 220x − x2 and limitations on space…

A: NOTE: Refresh your page if you can't see any equations. . to find the break-even, take P=0

Q: The demand and supply functions for your college newspaper are, q = −12,000p + 1,900 and q = 2,000p…

A: For neither shortage nor surplus,demand and supply must be equal

Q: If total costs are  C(x) = 300 + 260x  and total revenues are  R(x) = 300x − x2,  find the…

A:

Q: The total costs for a company are given by C(x) = 5400 + 20x + x2 and the total revenues are given…

A:

Q: The current situation of ABC company is as follows: Variable costs are 82% of sales and fixed costs…

A: Given: Variable costs are 82% of sales. fixed costs are $44000

Q: For a certain company, the cost function for producing x items is C(x)=30x+250 and the revenue…

A:

Q: If the demand for a pair of shoes is given by 2p + 5q = 200 and the supply function for it is p - 2q…

A: We are given, demand function : 2q+5q=200 -(i)                           Supply function : p-2q = 10…

Q: The profit function for a set of two electronics products can be expressed by the following…

A:

Q: The financial analysis department of a software design company determined that the cost of producing…

A: Given: C(x)=5000+3x p=23-x500 R(x)=px=23x-x2500

Q: A chemical manufacturer sells sulfuric acid in bulk at a price of $600 per unit. If the daily total…

A:

Q: A company operates two plants which manufacture the same item and whose total cost functions are C1…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: The marginal profit from selling x chairs is P'(x)=-10x2 +100x+50 dollars per chair. There are no…

A: The marginal profit from selling x chairs is P'(x)=-10x2 +100x+50 dollars per chair. There are no…

Q: If the total cost function for producing x lamps is C(x) = 360 + 35x + 0.4x2 dollars, producing how…

A:

Q: If the profit function for a firm is given by P(x) = -2400 + 140x - x and limitations on space…

A: Break- even point of the profit function

Q: Suppose a company's revenue function is given by R(q) = - q³ + 250q² and its cost function is given…

A: Given,          A company's revenue function is given by Rq=-q3+250q2 and its cost function…

Q: Suppose that the demand curve for corn has the equation p = - 0.17q + 6.389 and the supply curve for…

A: ven, equation of demand curve , p=-0.17q+6.389and , equation of supply curve , p = 0.2q +2.8

Q: If the demand for a pair of shoes is given by 2p+ 5q = 200 and the supply function for it is p-2q =…

A: In this question, we want to compare the quantity demanded and the quantity supplied for a pair of…

Q: in a monopoly market, the demand function for a product is p = 115 − 0.10x and the revenue function…

A:

Q: The market for a particular consumer good has a demand function given by: q = 24 - p and supply…

A: We have to calculate surplus

Transformation of Graphs

The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.

Exponential Functions

The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.