Suppose pq=100 is the demand equation for a manufacturer's product. Let C be the total cost, and assume that the marginal cost is 0.01 when q=200. Use the chain rule to find dc/dp when q=200*
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- A company produces and sells a consumer product and is able to control the demand for the product by varying the selling price. The approximate relationship between price and demand is p= 200-0.05D where p is the price per unit in dollars and D is the demand per month. The company is seeking to maximize its profit. The fixed cost is $15000 per month and the variable cost is $50 per unit. a. What is the number of units that should be produced and sold each month to maximize profit? b. What is the domain of profitable demand during a month? Show your spreadsheet.Showing your analytical work clearly in a step by step manner is a must. Otherwise points will be deducted. You can use Excel or any other graphing tool. A startup software company has indicated its cost, c(x), and revenue, f(x), as given below, such that x is the number of lines of programing code (units in 1000 lines). c(x) = 80000 - 2(x-200)2 f(x) = (x-10)3 + (x+10)2 Find the marginal cost analytically, and draw its graph Find the marginal revenue analytically, and draw its graph Solve for the x point where marginal cost is equal to marginal revenue analytically. Comment why is this point significant analytically. Write the profit function and draw its graph Is the profit function concave up or concave down? Answer all questions neatly pleaseAssume that it costs a company approximately C(x) = 400,000 + 180x + 0.001x² dollars to manufacture x smartphones in an hour. (a) Find the marginal cost function. Use it to estimate how fast the cost is increasing when x = 10,000. $ 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. The marginal cost from (a) is ---Select--- O than the average cost from (b). This means that the average cost is ---Select--- O at a production level of 10,000 smartphones.
- Pepper farming is carried out in a greenhouse. Proceeds from the sale of pepper, R,dollars per square meter is determined by the following function. R = 5T (1-e^-x) where T is the temperature set in the greenhouse (Celsius, C^0)and the amount of fertilizer per square meter (kilogram, kg) the costs are as follows: fertilizer cost per square meter is 20?, heating cost is 0.10^2.According to this information a) type the profit function of the manufacturer,?(?, ?).B) determine the end points of the profit function.c) show which endpoints you specify or which ones give the highest amount of fertilizer with the temperature value that makes the profit.The total cost and the total revenue (in dollars) for the production and sale of x ski jackets are given by C(x)=26x +18,625 and R(x)-200x-0.2x² for 0≤x≤ 1000. (A) Find the value of x where the graph of R(x) has a horizontal tangent line (B) Find the profit function P(x). (C) Find the value of x where the graph of P(x) has a horizontal tangent line. (D) Graph C(x), R(x), and P(x) on the same coordinate system for 0sxs 1000. Find the break-even points. Find the x-intercepts of the graph of P(x) (A) R(x) has a horizontal tangent line at x =Assume that it costs a company approximately C(x) = 400,000 + 160x + 0.002x2 dollars to manufacture x smartphones in an hour. (a) Find the marginal cost function. Use it to estimate how fast the cost is increasing when x = 10,000. $ 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. The marginal cost from (a) is --Select--- v than the average cost from (b). This means that the average cost is ---Select--- v at a production level of 10,000 smartphones. Need Help? Watch It
- Cost, revenue, and profit are in dollars and x is the number of units. A firm knows that its marginal cost for a product is MC = 2x + 25, that its marginal revenue is MR = 73 – 6x, and that the cost of production of 80 units is $8,560. (a) Find the optimal level of production. units (b) Find the profit function. P(x) = (c) Find the profit or loss at the optimal level. There is a -Select--- v of $The total cost (in hundreds of dollars) of producing x calculators per day is given by the equation. 20- 15- 10- C(x) = 6 + /2x + 32 Osx< 50 Perform the following calculations and interpret the results. 10 20 30 40 50 Production C'(x) =U %D Cost (hundred dollars)Cost, revenue, and profit are in dollars and x is the number of units.A firm knows that its marginal cost for a product is MC = 2x + 25, that its marginal revenue is MR = 43 − 4x, and that the cost of production of 80 units is $8,560. (a) Find the optimal level of production. units(b) Find the profit function. P(x) = (c) Find the profit or loss at the optimal level. There is a ---Select--- profit loss of $ .
- A company has cost and revenue functions, in dollars, given by C(q) = 6000 + 10g and R(q) – 12q . (a) Find the cost and revenue if the company produces 500 units. Does the company make a profit? What about 5000 units? Enter the exact answers. The cost of producing 500 units is $ The revenue if the company produces 500 units is $ | Thus, the company a profit. The cost of producing 5000 units is $ The revenue if the company produces 5000 units is s Thus, the company a profit. (b) Find the break-even point. Enter the exact answer. The break-even point is |units. Which of the following illustrates the break-even point graphically? 50000 R(g) C(q) 40000 30000 20000 10000 1000 2000 3000 4000 5000 50000 40000 30000 - 20000 10000 R(g) C(g) 1000 2000 3000 4000 5000A company produces and sells a consumer product and is able to control the demand by varying the selling price. The approximate relationship between price and demand is 2700 5000 p = 38 + (for D>1) D² The company is seeking to maximize its profit. The fixed cost is $1,000 and the variable cost is $ 40 per unit. What is the number of units and total amount that should be produced and sold each month to maximize profit?AVC=10-0.03Q + 0.00005Q2TFC=60What is the TC function?What is the minimum AVC?
