The cost of producing a units of a commodity is given by C(x) = 100+ 40x + 2x². (a) Find C(0), C(100), and C(101) - C(100). (b) Find C(x + 1) - C(x), and explain in words the meaning of the difference.
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- The cost of renting tuxes for the Choral Society's formal is $21 down, plus $87 per tux. Express the cost C as a function of x, the number of tuxedos rented. C(x) = Use your function to answer the following questions. (a) What is the cost of renting two tuxes? %$4 (b) What is the cost of the second tux? $4 (c) What is the cost of the 4,098th tux? 2$ (d) What is the variable cost? %24 What is the fixed cost? $4 What is the marginal cost? %241. The cost in dollars to produce x yards of a certain fabric is: C (x) = 84 + 0.16x - 0.0006x2 + 0.000003x3 a)Find the marginal cost function b)Find C '(x) and explain its meaning. What do you forecast? c)Compare C '(100) with the cost of making the 101-th yard.The table shows the marginal cost C'), the marginal revenue R'(x) for producing x items. The third column, P'(x). is partially completed. All values are in dollars per item. (a) Complete the remaining entries in the third column. (b) What does the table tell you about the revenue function? (c) Find the production level that maximizes profit. (a) Complete the remaining entries in the third column of the table on the right. c'(x) R'(x) P'(x) -21 62 41 (b) What does the table tell you about the revenue function? Select one and complete the box, if necessary. 10 41 41 40 14 41 O A. Items sell for $ each. 70 41 41 O B. There is not enough information to determine anything about the revenue function. 90 206 41 - 165 (c) Find the production level that maximizes profit. Profit P(x) is a maximum when x= items are produced.
- What is the difference between a price analysis and a cost analysisJenna knits scarves and then sells them on Etsy, an online marketplace. Let C(x) =4x+20 represent the cost C in dollars to produce 1 to 6 scarves. A.) Create a table to show the relationship between the number of scarves x and the cost C. B.) What are the domain and range of C? C.) What is the meaning of C(3)? D.) What is the meaning of the solution to the equation C(x) =40?The total cost of producing T-shirts can be represented as TC = 50 + 2Q. a) What is the marginal cost of the 5th T-Shrit? b) How much does it cost to produce 10 T-shirts?
- The variable x represents the number of HDTVs manufactured and sold in a given month. The variable p is the price charged when you sell a TV. A demand curve is given by p = 660-3x. a) Find the x-intercept of this demand curve. Say what it means. Assume you must pay salaries totalling 8000$ in a month. Also, it costs $110 to manufacture one TV. b) Write a formula for your cost function C(x) c) Write a formula for your revenue function R(x) d) The profit function is M(x) = Graph the profit function and using the Maximum program, find the maximum possible profit and fill in the details (round off x to the nearest whole number): e) number of sales: f) profit: g) selling price: h) revenue: i) cost: j) check these results fit together: k) Find the range of prices you can charge and still be in the black: The lowest price you can charge is ___________ and the highest is ___________A street musician bought a new fiddle for $850.00. Assume she breaks 1 string each hour and can buy new strings for $1.00 each. On average, she makes $18.00 per hour. (a) Find the cost function C(x) associated with playing the fiddle for x hours. C(x)= (b) Find the revenue function R(x) for the amount of revenue gained from x hours of playing R(x) = (c) Find the profit function P(x) for the amount of profit gained from x hours of playing P(x) = (d) Use the functions above to complete the following sentence. She will need to work hours to break evenConsider the following marginal cost function MC= 5 + 2qi. (a) Does the production process exhibits increasing returns? decreasing returns? constant returns? (b) If the price is $23. What’s the optimal production level? (c) If the price is $31. What’s the optimal production level?
- Suppose that the dollar cost of producing x appliances is c(x) = 1000 + 70x-0.1x². a. Find the average cost per appliance of producing the first 100 appliances. b. Find the marginal cost when 100 appliances are produced. c. Show that the marginal cost when 100 appliances are produced is approximately the cost of producing one more appliance after the first 100 have been made, by calculating the latter cost directly. CUCKO The average cost per appliance of producing the first 100 appliances is $ (Round to the nearest cent as needed.) /appliance.What is the wholesale cost of an item, if the retail cost is $62 and the amount of markup is $17? Use the formula R W + M (where R is the retail cost, W is the wholesale cost, and M is the amount of mark up). = The wholesale cost is dollars.1. If the cost function of producing a commodity is: 40 + 50x + Vx2 +1 10 C (x) = = where x represents the number of units produced. Calculate the marginal cost of producing 20 units.
