Suppose that the price p, in dollars, and the weekly sales x, in dozens of units,...
3) Suppose that the price p (in dollars) and weekly sales x (in 1000s) of light bulbs satisfy the demand equation 2p, + x2-275. Determine the rate at which sales are changing per week at a time when x-4, p-6, and price is falling at the rate of $0.30/week 4) If a cost function is Cx) ma find the marginal cost when x 3. Round you answer to 2 decimal places 5) Find the derivative: y = eB- 6) Show...
The weekly demand function is given by p + x + 4xp = 42, where x is the number of thousands of units demanded weekly and p is in dollars. If the price p is increasing at a rate of 26 cents per week when the level of demand is 3000 units, which one of the following statements is true? O Demand is increasing at 260 units per week O Demand is decreasing at 280 units per week O Demand...
5) When the price of a certain commodity is p dollars per unit, customers demand r hundred units of the commodity, where How fast is the demand r changing with respect to time when the price is $6 per unit and decreasing at the rate of 25 cents per month? 1 6) The output at a certain plant is Q-0.09r20.12ry+0.04y2 units per day, where z is the number of hours of skilled labor used and y is the number of...
5. Suppose that X the price of a certain commodity (in dollars), and Y, its total sales (in 10000 units), are random variables whose joint probability distribution is given by the following going PDF 5xe-rV :0.20< <0.40,y>0 x.y(x,y)ootherwise Use the CDF method to find and identify the distribution of V-XY, the total amount of money (in S10000 units) that is spent on this commodity
Suppose that the supply of x units of a product at price p dollars per unit is given by the following. p = 30 + 60 In(8x + 2) (a) Find the rate of change of supply price with respect to the number of units supplied. dp dx = (b) Find the rate of change of supply price when the number of units is 31. $ (c) Approximate the price increase associated with the number of units supplied changing from...
14. Suppose that when the price of a certain commodity is p dollars per unit, then x hundred units will be purchased by consumers, where = -0.05 x + 38 The cost of producing x hundred units is hundred dollars is C(x) = 0.02x2 + 3x + 574.77 hundred dollars a. Express the profit P obtained from the sale of x hundred units as a function of x. Sketch the graph of the profit function. b. Use the profit curve...
In this problem, p is in dollars and x is the number of units. Suppose the demand function for a product is p and the supply function is p = 1 + 0.2x. (x + 1) Find the equilibrium quantity. X1 - Find the equilibrium point. Find the consumer's surplus under pure competition. (Round your answer to the nearest cent.)
Let Qd be the number of units of a commodity demanded by consumers at a given time t and let Qsdenote the number of units of the commodity supplied by producers at a given time t. Let p be the price in dollars of the commodity at time t. Suppose the supply and demand functions for a certain commodity in a competitive market are given, in hundreds of units, by Qs = 30 + p + 5 dp/dt Qd =...
p ot an iten Hu between the price shows the relationship a demand curve on 3.5) In economics, the number x (in thousands) of such items that can be sold at that price. Suppose that the demand a commodity is given by the formula x2000-p3,valid for p S 12. Note that the radical in this equation is a cube root, not a square root.) (a) Use implicit differentiation to find the rate of change of p with respect to x...
The weekly demand function for x units of a product sold by only one firm is p = 600 – 3x dollars, and the average cost of production and sale is 7 = 400 + 2x dollars. (a) Find the quantity that will maximize profit. units (b) Find the selling price at this optimal quantity. per unit (c) What is the maximum profit?