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.
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- When sold for $790.00, a certain desktop has an annual supply of 129.5 million computers and an annual demand of 155.5 million computers. When the price increases to $865.00, the annual supply increases to 147.5 million computers, and the demand drops to 134.5 million computers. NOTE: Round slope and vertical intercept to 4 decimal places and use those rounded values to the end. (a) Assuming that the supply and demand equations are linear, find the supply and demand equations. Supply Equation p = Demand Equation p = esc (Note: The equations should be in the form p = mq + b where p denotes the price (in dollars) and q denotes the quantity (in billions). The slope and y-intercept should be accurate to 4 decimal places). (b) Find the Equilibrium price and quantity. Equilibrium price p = Equilibrium quantity q = 9- F2 A (Note: The equilibrium price should be accurate to 2 decimal places and quantity should be rounded to the nearest whole number, and the equilibrium price should include a…When the price of a gallon of milk increases from $6 to $8, quantity demanded decreases to 27 gallons. Assuming the price elasticity of demand for milk is -0.3, what is the original quantity demanded? (assuming further that this is the point elasticity relative to the original point on the demand curve.) Please make sure you give a numerical answer with no units and/or space or period (.) or comma (,) before or after your answer. Enter your answer hereThe quantity demanded x each month of Russo Espresso Makers is 250 when the unit price p is $150; the quantity demanded each month is 1000 when the unit price is $120. The suppliers will market 750 espresso makers if the unit price is $50. At a unit price of $80, they are willing to market 3000 units. Both the demand and supply equations are known to be linear. (a) Find the demand equation.p = (b) Find the supply equation.p = (c) Find the equilibrium quantity and the equilibrium price. equilibrium quantity units equilibrium price $
- The demand function for an item is given by d(x) = 100/ 0.01x 2 + 1 (20 ≤ x ≤ 50) where d(x) (measured in units of a thousand) is the quantity demanded per weak and x is the unit price in dollars. (a) Find the rate of change in demand with respect to price. (b) How fast is the demand changing at price equal to 30 (x = 30)?The demand function for a product is p= 45 5-9/10) where q is the number of units and p is the price of one unit. At what price will the demand be 5 units? How many units will be demanded if the price is $12.42?(a) Determine the equilibrium price and quantity.(b) Sketch the demand and supply functions on the same graph. Label theaxes and the intercepts clearly.
- 2) (20) Demand for widgets is a linear function of price. If the price of Widgets is set to $20, 4200 widgets will be sold. If the price is raised to $25, demand falls to 3600 widgets. a) (4) Find the demand function D(x), where x represents the price and D(x)= y represents the demand for widgets. b) (2) Describe the meaning of the slope of the demand function, in the context of the price, and demand for widgets. c) (2) Find the revenue function R(x), which is price times the demand. (2) Graph the Revenue Function using Desmos, or any other graphing utility of your choice; note the scale on the axes. If your graph doesn't fit on the graph, your Revenue function is probably incorrect. Hint Ask Questions! Email! 100000 90000 80000 70000 60000 50000 40000 30000 20000 10000 y -5 20 25 30 35 40 45 50 55 60 65 e) (2) Give the meaningful domain for the revenue function. Use the criteria that one would not price widgets so low that one would pay to get rid of them. 5 10 15 (2)Calculate the…Ammongas´'s demand depends on many factors, but can be presented in simplified form as: P = 8,000,000 - 240,000 * Q, where “Q” are standard plants sold per. year. Make a graphic illustration of the P-function, where it applies that the price can not be negative and a negative number of plants can not be demanded. Then derive the TR function and the MR function mathematically.The profit from the supply of a certain commodity is modeled as P(q) = 71ge-0.29 dollars where q is the number of units produced. 0 ≤ q ≤ 100 (a) Write an expression for the rate of change of profit. (Be sure to use q as the independent variable.) P'(q) dollars per unit (b) At what production level in the domain 0 ≤ q ≤ 100 is the rate of change of profit zero? (Round your answer to the nearest whole number.) q= units (c) What is profit at the production level found in part (b)? (Round your answer to two decimal places.)
- You have been hired as a marketing consultant to Johannesburg Burger Supply, Inc., and you wish to come up with a unit price for its hamburgers in order to maximize its weekly revenue. To make life as simple as possible, you assume that the demand equation for Johannesburg hamburgers is linear. (a) Your market studies reveal the following sales figures: When the price is set at $2.00 per hamburger, the sales amount to 2000 per week, but when the price is set at $4.00 per hamburger, the sales drop to zero. Use these data to find the linear demand function q(p), where p is the price per hamburger and q is the number of hamburgers they sell at that price per week. q(p) = X (b) Find the price elasticity of demand. E(p) X (c) When you raise the price by 1% from $2 per hamburger, the demand decreases Demand is of unit elasticity. V by 1 %.The demand function for a tablet is given by the model P= 200-16x2 where p is measured in dollars per tablet and x is measured in millions of tablets. If it costs $50 to produce each tablet and a profit of $125 million was derive when 2.5 million tablets were produced. Derive the number of tablets that the company could sell to make the same amount of profit?The revenue (in dollars) from the sale of x car seats for infants is given by the following function. R(x) = 56x – 0.020x? 0sxs 2800 (A) Find the average change in revenue if production is changed from 1,000 car seats to 1,050 car seats. (B) Use the four-step process to find R'(x). (C) Find the revenue and the instantaneous rate of change of revenue at a production level of 1,000 car seats, and interpret the results. (A) Find the average change in revenue if production is changed from 1,000 car seats to 1,050 car seats. (Round to one decimal place as needed.) (B) R'(X) = (C) R(1000) = R'(1000) = Interpret these results. Choose the correct answer below. O A. This means that at a production level of 1,000 car seats, the revenue is R(1000) dollars and is decreasing at a rate of R'(1000) dollars per seat. O B. This means that at a production level of 1,000 car seats, the revenue is R'(1000) dollars and is increasing at a rate of R(1000) dollars per seat. O c. This means that at a…