# The total revenue R (in dollars) is directly proportional to the number of units sold x. When 500 units are sold, the total revenue is $4825. Find a mathematical model that relates the total revenue R to the number of units sold x. Question Forms of linear equations asked 2020-10-23 The total revenue R (in dollars) is directly proportional to the number of units sold x. When 500 units are sold, the total revenue is$4825. Find a mathematical model that relates the total revenue R to the number of units sold x.

2020-10-24
Use the direct variation equation:
R=kx
When x=500, R=$4825 so we can solve for k: 4825=k(500) 4825/500=k 9.65=k So, the mathematical model is: R=9.65x ### Relevant Questions asked 2021-03-05 Suppose the manufacturer of widgets has developed the following table showing the highest price p, in dollars, of a widget at which N widgets can be sold. $$\begin{array}{|c|c|} \hline Number\ N & Price\ p\\ \hline 200 & 53.00\\ \hline 250 & 52.50\\\hline 300 & 52.00\\ \hline 350 & 51.50\\ \hline \end{array}$$ (a) Find a formula for p in terms of N modeling the data in the table. $$\displaystyle{p}=$$ (b) Use a formula to express the total monthly revenue R, in dollars, of this manufacturer in a month as a function of the number N of widgets produced in a month. $$\displaystyle{R}=$$ Is R a linear function of N? (c) On the basis of the tables in this exercise and using cost, $$\displaystyle{C}={35}{N}+{900}$$, use a formula to express the monthly profit P, in dollars, of this manufacturer as a function of the number of widgets produced in a month. $$\displaystyle{P}=$$ (d) Is P a linear function of N? asked 2021-02-25 In general, the highest price p per unit of an item at which a manufacturer can sell N items is not constant but is, rather, a function of N. Suppose the manufacturer of widgets has developed the following table showing the highest price p, in dollars, of a widget at which N widgets can be sold. $$\begin{array}{|c|c|} \hline Number\ N & Price\ p\\ \hline 250 & 52.50\\ \hline300 & 52.00\\\hline 350 & 51.50\\ \hline 400 & 51.00\\ \hline \end{array}$$ (a) Find a formula for p in terms of N modeling the data in the table. $$\displaystyle{p}=$$ (b) Use a formula to express the total monthly revenue R, in dollars, of this manufacturer in a month as a function of the number N of widgets produced in a month. $$\displaystyle{R}=$$ asked 2021-03-02 The cost in dollars to produce x youth baseball caps is C(x) = 4.3x + 75. The revenue in dollars from sales of x caps is $$\displaystyle{R}{\left({x}\right)}={25}{x}$$. (a) Write and simplify a function P that gives profit in terms of x. (b) Find the profit if 50 caps are produced and sold. asked 2020-11-06 A small grocer finds that the monthly sales y (in$) can be approximated as a function of the amount spent advertising on the radio $$x_1$$
(in $) and the amount spent advertising in the newspaper $$x_2$$ (in$) according to $$y=ax_1+bx_2+c$$
The table gives the amounts spent in advertising and the corresponding monthly sales for 3 months.
$$\begin{array}{|c|c|c|}\hline \text { Advertising, } x_{1} & \text { Advertising, } x_{2} &\text{sales, y} \\ \hline  2400 & { 800} & { 36,000} \\ \hline  2000 & { 500} & { 30,000} \\ \hline  3000 & { 1000} & { 44,000} \\ \hline\end{array}$$
a) Use the data to write a system of linear equations to solve for a, b, and c.
b) Use a graphing utility to find the reduced row-echelon form of the augmented matrix.
c) Write the model $$y=ax_1+bx_2+c$$
d) Predict the monthly sales if the grocer spends $250 advertising on the radio and$500 advertising in the newspaper for a given month.
Let's say the widget maker has developed the following table that shows the highest dollar price p. widget where you can sell N widgets. Number N Price p $$200 53.00$$
$$250 52.50$$
$$300 52.00$$
$$35051.50$$ (a) Find a formula for pin terms of N modeling the data in the table. (b) Use a formula to express the total monthly revenue R, in dollars, of this manufacturer in month as a function of the number N of widgets produced in a month. $$R=$$ Is Ra linear function of N? (c) On the basis of the tables in this exercise and using cost, $$C= 35N + 900$$, use a formula to express the monthly profit P, in dollars, of this manufacturer asa function of the number of widgets produced in a month $$p=$$ (d) Is Pa linear function of N2 e. Explain how you would find breakeven. What does breakeven represent?
Suppose a nonhomogeneous system of nine linear equations in ten unknowns has a solution for all possible constants on the right sides of the equations. Is it possible to find two nonzero solutions of the associated homogeneous system that are not multiples of each other? Discuss.
Determine whether each of the given sets is a real linear space, if addition and multiplication by real scalars are defined in the usual way. For those that are not, tell which axioms fail to hold. All vectors (x, y, z) in $$V_3$$ whose components satisfy a system of three linear equations of the form:
$$a_{11}x+a_{12}y+a_{13}z=0$$
$$a_{21}x+a_{22}y+a_{23}z=0$$
$$a_{31}x+a_{32}y+a_{33}z=0$$
The purchase price of a home y (in $1000) can be approximated based on the annual income of the buyer $$x_1$$ (in$1000) and on the square footage of the home $$x_2 (\text{ in } 100ft^2)$$ according to $$y=ax_1+bx_2+c$$
c) Write the model $$y=ax_1+bx_2+c$$
d) Predict the purchase price for a buyer who makes $100000 per year and wants a $$2500ft^2$$ home. asked 2021-03-07 Mathematical modeling is about constructing one or two equations that represent real life situations. What are these math models used for? Provide at least two equations that can be used in the real world. For example: The equation $$s = 30\ h\ +\ 1000$$ can be used to find your salary given the fact you earn a fixed salary of$1000 per month, plus \$30 per hours. Here s represents the total salary and h is the number of hours you worked.