The marketing research department for the company that manufactures and sells “notebook” computers established the following price – demand function:
ters established the following price – demand function:
p(x) = 10 – 0,001x, where p(x) is the wholesale price in dollars at which x thousand computers can be sold.
Total cost (in dollars) of producing x items is given by C(x) = 7000 + 2x.
A) Find the revenue function and state its domain.
B) Find the marginal revenue function. Find R´(4000) and R´(6000). Interpret the results.
C) Evaluate the approximate revenue and exact revenue of producing 101-th notebook.
D) Find the profit function
E) Find the marginal profit function.
F) Evaluate the approximate profit and exact profit of producing 101-th notebook.
G) Find P´(5000) and P´(7000). Interpret the results.
3.Suppose that Wegboys has a supermarket with a downward sloping demand curve in Pilgrim City. It purchases frozen turkeys
chases frozen turkeys at a constant wholesale price of $1/turkey, which is its full marginal cost for supplying turkeys. During July, only a small number of wealthy people are interested in buying turkeys in Pilgrim. Their demand curve is P = 10 – .02 Q, where P is Wegboys’ retail price for turkeys during the month and Q is the quantity of turkeys purchased. The demand curve for these wealthy people is constant – it is the same curve in both November and July. During November, a large number of less wealthy people enter the market to purchase turkeys for Thanksgiving. Their demand curve for Wegboys’ turkeys is
P = 4 – .0005Q. In other months of the year, they do not purchase turkeys at any price.
a. (5 points) What price should Wegboys charge in July to maximize its profits? Calculate its profits from turkey sales.
b. (5 points) Demonstrate that Wegboys can earn a higher profit if it lowers its retail price for turkeys during November (you can do this without finding the optimal price). Explain the basic economic intuition.
4.1. The marginal cost of making x^th chai tea lattes is given by M(x)=20/x^2. Find the total cost accrued when
rued when you go from making 1 chai tea latte a day to 40 chai tea lattes a day. (Hint: relationship between marginal cost and total cost)
2. Suppose that C(x) = -0.01x + 5 represents the daily cost of heating the doughnut shop, in dollars per day, where x is time in days and x = 0 corresponds to January 1, 2020. Find the total cost of heating the shop for the first two weeks of January, and find the average cost to heat the shop each day for the first two weeks of January.