Al's production function for deer is f(x1,x2) = (2x1 + x2)^1/2, where x1 is the amount of plastic and x2 is the amount of wood used. If the cost of plastic is $4 per unit and the cost of wood is $3 per unit, then the cost of producing 5 deer is a) $55 b) $10 c) $50 d) $75
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- (a) The cost of producing 5-gallon water bottles is given by C(q) = 0.005q² + 2q + 1000. If 2000 5-gallon water bottles are produced, find the %3D (i) total cost (ii) average cost (iii) marginal cost (iv) marginal average cost SBx2 -3 (Bx+2 (b) Suppose that f(x) if X 2 Find the value of B so that f(x) is continuous everywhere along the real line. (c) The demand for watches is given by p = 7000 - 2q dollars, and the supply of watches is given by p 0.01q? + 2q + 1000 dollars, %3D where q is the number of watches demanded and supplied when the price per watch is p dollars. Based on the information provided, calculate the equilibrium quantity and the equilibrium price for watches.Assume that it costs a company approximately C(x) = 400,000 + 140x + 0.003x? dollars to manufacture x smartphones in an hour. (a) Find the marginal cost function. 400,000 – 0.000009 Use it to estimate how fast the cost is increasing when x = 10,000. 2$ 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 isThe 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)
- A 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.) $ 4.56Cost, revenue, and profit are in dollars and x is the number of units. A firm knows that its marginal cost for a product is МС- 4x+ 25, that its marginal revenue is MR%3D 75 - 6х, and that the cost of production of 60 units is $8,880. (a) Find the optimal level of production. units (b) Find the profit function. P(x) = (c) Find the profit or loss at the optimal level.The profit of a company, in dollars, is the difference between the company's revenue and cost. The cost, C(x), and revenue, R(x), are functions for a particular company. The x represents the number of items produced and sold to distributors. C(x) = 2500 + 60x R(x) = 800x - x? a) Determine the maximum profit of the company. The maximum profit of the company is b) Determine the number of items that must be produced and sold to obtain the maximum profit. The number of items that must be produced and sold to obtain the maximum profit is
- The profit (in dollars) from the sale of x lawn mowers is P(x)= 20x - 0.02x^2 - 650 (A) Find the average profit per mower if 60 mowers are produced (B) Find the marginal average profit at production level of 60 mowers, and interpret results (C)Use the results from parts A and B to estimate the average profit per mower if 61 mowers are produced (1. Exercise 9.1 A study of 86 savings and loan associations in six northwestern states yielded the following cost function. 2.38 0.006153Q 0.000005359Q² 19.2X1 C + + (2.62) (2.84) (3.16) (3.50) where C = average operating expense ratio, expressed as a percentage and defined as total operating expense ($ million) divided by total assets ($ million) times 100 percent. Q = output; measured by total assets ($ million) X1 = ratio of the number of branches to total assets ($ million) Note: The number in parentheses below each coefficient is its respective t-statistic. Which of the variable(s) is (are) statistically significant in explaining variations in the average operating expense ratio? (Hint: t0.025,7€ 1.99 .) Check all that apply. X1 Q2 What type of average cost-output relationship is suggested by these statistical results? Quadratic Linear Cubic Based on these results, what can we conclude about the existence of economies or diseconomies of scale in savings and loan associations in…A heavy equipment manufacturing company has produced its first unit using 3500 hours and $300,000 overhead cost. The next unit, i.e. the second unit took 3300 hours. Overhead cost for this unit was $200,000. Suppose the labor was $20 per hour. Being the production manager, you need to decide what would be the total production costs for additional 10 units after the completion of the second unit. Round the final amount to nearest integer. $1,597,832 C$1,003,183 (DNone of the above
- The total profit P(x) (in thousands of dollars) from the sale of x hundred thousand pillows is approximated by P(x) = -x° + 12x + 144x – 400, x25. Find the number of hundred thousands of pillows that must be sold to maximize profit. Find the maximum profit. The maximum profit is $ The maximum profit will occur when pillows are sold.A 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?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?
