In this problem, p is in dollars and q is the number of units. Suppose that the demand for a product is given by

pq + p + 100q = 50,000.

(a) Find the elasticity when

p = $568.

(Round your answer to two decimal places.) (b) Tell what type of elasticity this is. Demand is elastic.Demand is inelastic. Demand is unitary elastic. (c) How would a price increase affect revenue? An increase in price will result in an increase in total revenue.Revenue is unaffected by price. An increase in price will result in a decrease in total revenue.

HARMATHAP12 10.3.039.EP. The monthly demand function for a product sold by a monopoly is p : 2,140 x2 dollars, and the average cost isE : 1,000 + 8x + x2 dollars. Production is limited to 1,000 units, and x is in hundreds of units. Find the revenue function, R(x). Rm = Find the cost function, C(X). C(X) = Find the profit function, P(X). P(X) = (a) Find pm. P'(X) = Considering the limitations of production, nd the quantity (in hundreds of units) that will give the maximum profit. S hundred units (b) Find the maximum profit. (Round your answer to the nearest cent.) $: Submit Answer HARMATHAP12 9.6.011.Ml. Differentiate the function. 2 f : 7 (5) (257 + n4 f'(s) : DETAILS HARMATHAP12 9.1.021.MI. Use properties of limits and algebraic methods to find the limit, if it exists. (If the limit is infinite, enter '.' or '-co', as appropriate. If the limit does not otherwise exist, enter DNE.) lim x2 - 36 x - -6 x+6 5. DETAILS HARMATHAP12 13.3.007. Consider the following. 4 y = x+2 3 y = x2 - X 1 2 (a) Find the points of intersection of the curves. (x, y) = ( (smaller x-value) (x, y) = ( (larger x-value) (b) Form the integral that represents the area of the shaded region. (c) Find the area of the shaded region.DETAILS HARMATHAP12 11.2.023. Find the derivative of the function. y = In(ex + 9) DETAILS HARMATHAP12 13.2.025. Evaluate the definite integral. V3 x + 16 dx DETAILS HARMATHAP12 12.2.023. Evaluate the integral. Check your result by differentiation. (Remember the constant of integration.) 2x 8 V x 8 + 3 dx 10 DETAILS HARMATHAP12 12.4.022. Suppose that the marginal propensity to consume is "C = 0.2 - e-0.5y dy (in billions of dollars) and that consumption is $9.5 billion when disposable income is $0. Find the national consumption function. C(y) =6. DETAILS HARMATHAP12 10.1.011. Consider the following. y = x' - 3x + 5 y 10 HNW PU -4 -3 1-2 -1 1 2 3 -1 -2 - 3- -4L (a) Estimate the coordinates of the relative maxima, relative minima, or horizontal points of inflection by observing the graph. (If an answer does not exist, enter DNE.) relative maxima ( x, y ) = relative minima ( x, y ) = horizontal points of inflection ( x , y ) = (b) Use y' = f'(x) to find the critical values. (Enter your answers as a comma-separated list.) X = (c) Find the critical points. (Order your answers from smallest to largest x, then from smallest to largest y.) ( x, y ) = ( ( x, y ) =