Tesla estimates that its profit expressed in thousands of dollars each month is given by the expression: -6q^2 + 30q + 3210 where q (in thousands) is the number of cars produced and sold in a month. Determine the following: a. If Tesla's cost function is C(q) = 3210, state Tesla's variable cost per car. B.If Tesla wishes to make a profit greater than $2,910,000, calculate and state the interval of value(s) for which this goal can be achieved.

Tesla estimates that its profit expressed in thousands of dollars each month is given by the expression: -6q^2 + 30q + 3210 where q (in thousands) is the number of cars produced and sold in a month. Determine the following: a. If Tesla's cost function is C(q) = 3210, state Tesla's variable cost per car. B.If Tesla wishes to make a profit greater than $2,910,000, calculate and state the interval of value(s) for which this goal can be achieved.

Microeconomics

13th Edition

ISBN:9781337617406

Author:Roger A. Arnold

Publisher:Roger A. Arnold

Chapter8: Production And Costs

Section: Chapter Questions

Problem 5WNG

See similar textbooks

Similar questions

Given the following cost functions: TC=100+60Q-3Q2+0.1Q3 TC=100+ 60Q+3Q2 TC=100 + 60Q Compute the average variable cost, average cost, and marginal cost for each function. Plot them on a graph. In each case, indicate the point at which diminishing returns occurs. Also, indicate the point of maximum cost efficiency (i.e., the point of minimum average cost). What is the relationship between marginal cost and average variable cost and between marginal cost and average cost? What is the relationship between average variable cost and average cost?
A skateboard manufacturer produces skateboards at a cost of $45 each, with a monthly fixed cost of $9000. Let x be the number of boards manufactured in a month. Write a function C(x) that represents the total cost of producing x boards. A/ Write a function A(x) that represents the average cost per skateboard each month. A/ Find the equation of the horizontal asymptote of A(x). A .D
Let C(T) be a function that models the dependence of the cost (C) in thousands of dollars on the amount of ore to extract from a copper mine measured in tons (T): 1) If you computed the average rate of change of cost with respect to tons for production levels between T = 20000 and T = 40000, give the units of your answer (no calculations - describe the units of the rate of change). 2) If you had a function for C(T) and were able to calculate the answer to part 1, explain why you would not expect your answer to be negative (explanation should be in terms of cost, tons of ore to extract, and rates of change).
Give the formulas for and plot AFC, MC, AVC, and AC if the cost function is a C = 10+10q (MC = 10) b C = 10 + q2 (MC=2q). c C = 10 + 10q - 4q2 + q3 (MC = 10 - 8q + 3q2). ATC AVC AFC
The estimated cost to produce x items is given by the function: C(x) = 0.004x² + 5x + 6000 Determine the average cost and marginal cost of producing 2,000 items and calculate the level of output for which the average cost is the lowest and what that cost is.
Consider the following cost function: C= 0.25q - 49° + 85q + 150: When output is 16 units, average cost is $ (Enter a numeric response using a real number rounded to two decimal places.) When output is 16 units, marginal cost is $ The output level where average variable cost equals marginal cost is units. 20 tv MacBook Air 80 DII F2 F3 F4 FB F10 F11 %23 $ & 3 4 5 8 { [ ン E R Y U P D F G K C V N M command option .. .. ト
Jason owns a lamp store. His total costs are $145,000 per year, and his fixed cost are $19,200. His production is 12,500 per year. This means that his average variable is how much? (hint: enter your answer in two decimals) The answer should be 10.06, please explain how to get to the answer
The hourly operating cost of a plane which seats up to 405 passengers is estimated to be $5,328. If an airline charges each passenger a fare of $120 per hour of flight, find the hourly profit P it earns operating the plane as a function of the number of passengers x. [HINT: The cost function is constant (variable cost = 0).] P(x) = Specify the domain. (Enter your answer using interval notation.) What is the least number of passengers the plane must carry to make a profit? (Round your answer up to the nearest whole number.) passengers
As a producer and seller of some commodity, you have learned that, if you produce and sell x itmes in a particular month, the following functions can be used to find the cost and revenue: Revenue: R(x)=150x-x^2 and Cost: C(x)=3000+20x. (a) Write a simplified formula for your profit in a particular month, P(x)=R(x)- C(x) (b) Find the "break-even" point(s) (c) How many items should you produce and sell in a month in order to achieve a maximum profit? (d) What is the maximum possible monthly profit? This is the problem and I cannot solve the c and d, could you please help me?
E Let the demand function for a product be given by the function D(q) = -1.65g + 270, where q is the quantity of items in demand and D(q) is the price per item, in dollars, that can be charged when q units are sold. Suppose fixed costs of production for this item are $4, 000 and variable costs are $3 per item produced. If 96 items are produced and sold, find the following: A) The total revenue from selling 96 items (to the nearest penny). Answer: $ B) The total costs to produce 96 items (to the nearest penny). Answer: $ C) The total profits to produce 96 items (to the nearest penny. Profits may or may not be negative.). Answer: $ Question Help: C ME PE Video 66°F Mostly cloudy
Give the formulas for average fixed cost (AFC), marginal cost (MC), average variable cost (AVC), and average cost (AC) if the cost function is: 26.00 24.00- C=6+13q. 22.00 Average fixed cost is: 20.00- 18.00 AFC = * 16.00 Marginal cost is: 14.00- MC = 10.00 Average variable cost is: 8.00 6.00- AVC = 4.00 Average cost is: 2.00 0.00- AC =D Quantity, q. Units per day 1.) Use the line drawing tool to draw the marginal cost curve. Label this line 'MC'. If you are viewing this on a test or quiz, you must click the graph to enable the drawing tools. 2.) Use the 3-point curved line drawing tool to draw the average cost curve for quantities q= 1, q = 2, and q = 3. Label this curve 'AC'. Carefully follow the instructions above, and only draw the required objects. étv 20 MacBook Air S0 DII F3 F4 FS F6 F7 FB F9 2$ & 3 4 7 8 9 { [ W E R T Y U P D F G H J K ? C V N command option .. .. Cost per unit, $ * 0O
The profit of a company, in dollars, is the difference between the company's revenue and cost. The cost, C(x), and revenue, R(x), are functions for a particular company. The x represents the number of items produced and sold to distributors. C(x)=-2300+40x R(x)=840x-x² a) Determine and simplify the profit function. Write your answer in descending order. P(X)-