Suppose that the supply and demand equations for a certain product are given by: p=D(q)=70-0.2x p=S(q) 13+0.004.x² Graph the two functions on the same axes. Label some of the values on each axis.

A rental car company has a special deal on one of the available rentals. Let C be the cost, in dollars, of the rental car as a function of the distance d, in miles, it is driven in one day. A. What would the value C(75) represent in this context? B. Is function Cincreasing or decreasing? What are the units of the slope in this situation? C. Identify any maximum or minimum values of the function. What do they represent in this situation? State any assumptions that you make. D. Would the graph of C have any intercepts? What would they represent in this situation? E. Write a rule for C(d), and sketch a graph of the function.

A small company produces organic cookies. When the price is $6 per dozen, the average daily sales has been 72 dozen cookies. When the price was decreased to $3 per dozen, the average daily sales increased to 110 dozen cookies. Assume that daily cookie sales is linearly related to price per dozen. Each dozen cookies has a variable cost of 87 cents to make, plus additional daily fixed costs of $84. Find a function that models the daily profit in terms of the sales x in dozens of cookies.

Which of the following is true? OA. Quantity rises and the effect on price is unknown B. Quantity is unknown and price rises OC. Quantity rises and price falls OD. Quantity and price rise q

I need some help  Consider the equations and graphs for the demand and supply functions given below. Then answer the following questions. P=5Q^2+72Q P=-Q^2-3Q+20.23 State the domain for these curves for the analysis to be valid. (Answer to 2 decimal places)

f(x1,x2) 4 2 0 -2 -4 −1 2 0 1 1 0 2 -1 X1 3-2 x2 Figure 2: Graph of the function f(x1, x2) = 2x1 = x²-x+3 Consider the following function: f(x1, x2) = 2x1 - x-x+3. - For your visual convenience, a portion of the function is depicted in Figure 2. (a) Compute the gradient vector of f. (b) Compute the Hessian matrix of f. (c) Determine all points that yield stationary values of f. (d) Use the second-order conditions to determine whether each of the stationary val- ues of f is a maximum, a minimum, or neither.

A lake has two species of fish: bass and catfish. The number of bass and catfish living in the lake, B and C respectively, depend on the temperature of the lake, T (in degrees Farenheit). The functions modeling this dependency are given below: B(T) = 8T2 + 976T – 28890 С(Т) 3D — 2T?+244T — 6893 What are the two temperatures at which the number of bass in the lake is the same as the number of catfish? Enter exact expressions or round your answers to the nearest thousandth. T : T

A firm has the production function f(X, Y) = x²/2 y1/2, where X is the amount of factor x used and Y is the amount of factor y used. On a diagram we put X on the horizontal axis and Y on the vertical axis. We draw some isoquants. Now we draw a straight line on the graph and we notice that wherever this line meets an isoquant, the isoquant has a slope of -3. The straight line we drew Select one: O a. is vertical. b. is horizontal. c. is a ray through the origin with slope 3. d. is a ray through the origin with slope 4. O e. has a negative slope.

Consider the linear spline function f(x) = 1 + x + h1(x, 2) where h1(x,2) = x-2 if x>2 and 0 otherwise. What is the slope of f at the point x=-1?

e Price -Q₁ Quantity Which of the following scenarios is BEST represented in the graph? A number of sellers increase B decrease in government taxes C resource costs increase D technology improves