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.
4.The cost of gym membership, C, in Australian dollars (AUD), in Paolo’s Gym can
be modelled by the function
C = 65t
C = 65t + 30
where t is the time in months.
(a) Calculate the gym membership cost over a six month period.
(b) Sketch the graph of the function C = 65t + 30 for t ≥ 0.
(c) Calculate the time, t, in months, when the total cost reaches 290 AUD.
In the neighbouring Nicolo’s Gym, the initial payment is 75 AUD higher than in
Paolo’s Gym, however the monthly fee is lower at 30 AUD per month.
(d) Determine the number of months it takes for the total cost to be less by
attending Nicolo’s Gym in comparison to Paolo’s Gym.
8.1. 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.