. If the production function is given by f(x1,x2, x3, x4) = min{x1, x2} + min{x3, x4} and the prices of inputs (x1,x2, x3, x4) are (2, 1, 5, 3), the minimum cost of producing 1 unit of output is closest to a. $1. b. $3. C. $4. d. $8. e. $11. ANS:
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- A company is planning to manufacture mountain bikes. The fixed monthly cost will be $100,000 and it will cost $100 to produce each bicycle. A. Write the cost function, C, of producing x mountain bikes per month. C(x) = B. Write the average cost function, C, of producing x mountain bikes per month. C(x) = C. Find and interpret C(500), C(1000), C(2000), and C(4000). C(500) = Interpret C(500). When bicycles are produced in a month, it costs $ to produce each bicycle. C(1000) = Interpret C(1000). When bicycles are produced in a month, it costs $ to produce each bicycle. C(2000) = Interpret C(2000). When bicycles are produced in a month, it costs $ to produce each bicycle. Click to select your answer(s). (99+(a) Find the marginal cost function C'(x). C'(x) Use it to estimate how fast the cost is increasing when x = 60,000. | per game system Compare this with the exact cost of producing the 60,001st game system. The cost is increasing at the rate of $ | game system is $| the estimated cost of producing the 60,001st game system found using the marginal cost function. | per game system. The exact cost of producing the 60,001st J. The actual cost of producing the 60,001st game system is --Select-- (b) Find the average cost function C(x) and the average cost to produce the first 60,000 game systems. (Round your answer to the nearest cent.) C(x) C(60,000) - $ (c) Using your answers to parts (a) and (b), determine whether the average cost is rising or falling at a production level of 60,000 game systems.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.
- Suppose the fixed cost of building a nuclear power plant is $1 billion. Suppose also that the only variable cost is the labor of Homer Simpson, and he earns $10 per hour. If the plant generates 1,000 kilowatts each hour, and has already generated 1 billion kilowatts, what can you say about the marginal cost of the next kilowatt? (A) The marginal cost is equal to $0.01. (B) The marginal cost is equal to $1.01. D The marginal cost is falling. The marginal cost is rising.Suppose that the cost function for a commodity is C(x) = 40 + x2 dollars. (a) Find the marginal cost at x = 4 units. MC(4) = Tell what this predicts about the cost of producing 1 additional unit. The cost to produce the 5th unit is predicted to be $ (b) Calculate C(5) – C(4) to find the actual cost of producing 1 additional unit. Need Help? Read It Watch ItAs a production process requires labor L and capital K, q = F (L, K). The wage for a labor is $500, the cost for one capital is $250. If the production plan is to produce 250 products, what is the firm's minimized cost? A: $7500 B: $5000 C: $12500 D: $10000
- The total cost (in dollars) of producing x food processors is C(x) = 1600 + 40x-0.1x². (A) Find the exact cost of producing the 61st food processor. (B) Use the marginal cost to approximate the cost of producing the 61st food processor. CHEO (A) The exact cost of producing the 61st food processor is $ (B) Using the marginal cost, the approximate cost of producing the 61st food processor is $1/3 1/3 Farmer Joe's production function is f(x1, x2) = ", where xị is the number of pounds of lemons he uses and x2 is the number of hours he spends 1/21/2 2wi"wy3/2, where y is the squeezing them. His cost function is c(w1. w2, y) = number of units of lemonade produced. (a) If lemons cost $1 per pound, the wage rate is $1 per hour, and the price of lemonade is p, what is his marginal cost function?It costs a baker a fixed cost of $420 and a variable cost of $2.10 per cupcake. A cupcake is sold for $4.90 each. (i) Make a table showing the cost of producing 20,40,60,80 and 100 cupcakes. (ii) Make a table showing the revenue from selling 20,40,60,80 and 100 cupcakes. (iii) Write an algebraic expression representing the cost C as a function of the number of cupcakes x that are produced. (iv) Write an algebraic expression representing the revenue R as a function of the number of cupcakes x sold. (v) Graph both functions on the same coordinate axes. (vi) From your graph find coordinates at which cost equals revenue. (vii) Using your graph, determine how many cupcakes need to be made to produce revenue of at least $1,029.How much profit is made for this number of cupcakes?
- A company manufactures mountain bikes. The research department produced the marginal cost function C'(x)=500-3, 0≤x≤ 900, where C'(x) is in dollars and x is the number of bikes produced per month. Compute the increase in cost going from a production level of 450 bikes per month to 600 bikes per month. Set up a definite integral and evaluate it. ← The increase in cost is $Consider the following cost function. a. Find the average cost and marginal cost functions. b. Determine the average and marginal cost when x = a. c. Interpret the values obtained in part (b). C(x) = 0.04x³ +0.4x² + 30x+130, 0≤x≤ 1500, a = 1000 a. The average cost function is C(x)=When a toy factory makes x dolls a day their total cost is C(x) = 50 + 9x + 0.02xr² dollars. What is the average cost of a doll when 58 dolls are made in one day? a. b. What is the marginal cost when 58 dolls are made in one day?
