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- 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?It costs a baker a fixed cost of $420 and variable cost of $2.10 per cupcake. A cupcake issold for $4.90 each.(i) Make a table showing the total cost and the revenue obtained from producing 20,40,60,80 and 100 cupcakes.(ii) Write algebraic expressions representing the cost C and the revenue R as functions of the number of cupcakes X produced and number of cupcakes X sold respectively.(iii) Graph both functions on the same coordinate axes and from your graph determine the cordinate at which cost equals revenue.Please I need help on the math question I don't ge it Suppose that the monthly cost, in dollars, of producing x chairs is C(x)=0.005x3+0.07x2+15x+600, and currently 35 chairs are produced monthly. a) What is the current monthly cost? b) What is the marginal cost when x=35? c) Use the result from part (b) to estimate the monthly cost of increasing production to 37 chairs per month. d) What would be the actual additional monthly cost of increasing production to 37 chairs monthly?
- Use the equations for the total cost C and total revenue R to find the number x of units a company must sell to break even. (Round to the nearest whole unit.) C = 8950x + 220,000, R = 9857xA cost function is given. C(q) = 3600 + 5q-0.02q² + 0.00039³ (a) Find the average cost and marginal cost functions. +5 -0.02q +0.0003q average cost 3600 9 marginal cost 5 -0.04q+0.0009q (b) Use graphs of the functions in part (a) to estimate the production level that minimizes the average cost. (Round your answer to the nearest integer.) 194 ✓ units (c) Use calculus to find the minimum average cost. (Round your answer to two decimal places.) $ 32.41 X (d) Find the minimum value of the marginal cost. (Round your answer to two decimal places.) $ 4.56Assume that it costs a company approximately C(x) = 400,000 + 140x + 0.003x? dollars to manufacture x smartphones in an hour. (a) Find the marginal cost function. 400,000 – 0.000009 Use it to estimate how fast the cost is increasing when x = 10,000. 2$ per smartphone Compare this with the exact cost of producing the 10,001st smartphone. The cost is increasing at a rate of $ per smartphone. The exact cost of producing the 10,001st smartphone is $ Thus, there is a difference of $ (b) Find the average cost function C and the average cost to produce the first 10,000 smartphones. C(x) = C(10,000) = $ (c) Using your answers to parts (a) and (b), determine whether the average cost is rising or falling at a production level of 10,000 smartphones. -Select--- at a production level of 10,000 smartphones. The marginal cost from (a) is --Select--- than the average cost from (b). This means that the average cost is
- Additionally, what is the maximal profit?The total revenue function for a product is given by R=655x dollars, and the total cost function for this same product is given by C=19,250+70x+x2, where C is measured in dollars. For both functions, the input x is the number of units produced and sold. a. Form the profit function for this product from the two given functions. b. What is the profit when 25 units are produced and sold?(b) The total revenue curve of a firm is R(q) = 40q – 12q² and its q- 12.85q + 20 + 30 400 where q is the firm's output. average cost A(q) Derive an expression C(q) for the firm's total cost function. Derive an expression II(q) for the firm's profit function. iii. Is the rate of change of profit increasing or decreasing when the ouput level of the firm is 10 units? iv. Determine the level of output for which the firm's profit is maximize v. What is the firms's maximum profit? i. ii.
- What is the formulae used to find unit cost?Revenue and Cost The total weekly revenue functionfor a certain digital camera is given by R = 550xdollars, and the total weekly cost function for thecameras is C = 10,000 + 30x + x2dollars, where xis the number of cameras that are produced and sold.a. Find the profit function.b. Find the number of cameras that gives maximumprofit.c. Find the maximum possible profit.The cost, in millions of dollars, of building a three-story high school in NewYork State was estimated to be: 2C x x x x 1.7 0.14 0.0001 20 400where x is the number of thousands of square feet. Suppose that you arecontemplating building a for-profit three-story high school and estimate thatyour total revenue will be $0.2 million dollars per thousand square feet.(a) What is minimum area for a three-story high school in New YorkState, that this model covers? (b) What is the variable cost of building a three-story high school in NewYork State? (c) What is the fixed cost of building a three-story high school in NewYork State? (d) Determine the profit function,P x( ), for building a three-story highschool in New York State? . (e) Determine,P(250) , for building a three-story high school in New YorkState, and interpret the result. (f) How many thousands of square feet should a three-story high schoolbuilding in New York State be in order to break even?