Consider the technology function f(z1,z2) = 2zk + zk. Suppose that w] = 64, that w2 = 52, and that you need to produce output q = 1760. a) `When k = 1, cost is minimised at z1 = and z2 = b) c), When k = 2, cost is minimised at z1 = When k = 0.5, cost is minimised at z1 = and z2 = and z2 =
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- A small bank is trying to determine the number of tellers to employ. The total cost of employing a teller is $100 per day, and a teller can serve an average of 160 customers per day. On average, 210 customers arrive per day at the bank, and both service times and interarrival times are exponentially distributed. If the delay cost per customer day is $200, how many tellers should the bank hire?Suppose a Cobb-Douglas Production function is given by the function: P(L,K)=8L^0.7K^0.3Furthemore, the cost function for a facility is given by the function:C(L,K)=300L+500KSuppose the monthly production goal of this facility is to produce 20,000 items. In this problem, we will assume LL represents units of labor invested and KK represents units of capital invested, and that you can invest in tenths of units for each of these. What allocation of labor and capital will minimize total production Costs?Units of Labor LL = (Show your answer is exactly 1 decimal place)Units of Capital KK = Incorrect (Show your answer is exactly 1 decimal place)Also, what is the minimal cost to produce 20,000 units? (Use your rounded values for LL and KK from above to answer this question.)The minimal cost to produce 20,000 units is $ Hint: Your constraint equation involves the Cobb Douglas Production function, not the Cost function. When finding a relationship between LL and KK in your system of…The total cost C for a manufacturer during a given time period is a function of the number N of items produced during that period. To determine a formula for the total cost, we need to know two things. The first is the manufacturer's fixed costs. This amount covers expenses such as plant maintenance and insurance, and it is the same no matter how many items are produced. The second thing we need to know is the cost for each unit produced, which is called the variable cost.Suppose that a manufacturer of widgets has fixed costs of $1000 per month and that the variable cost is $20 per widget (so it costs $20 to produce 1 widget). Explain why the function giving the total monthly cost C, in dollars, of this widget manufacturer in terms of the number N of widgets produced in a month is linear. C always increases by $20 when N increases by ______. Therefore, C has a constant rate of change and so is a linear function of N. Identify the slope and initial value of this function. slope…
- Let C(T) be a function that models the dependence of the cost (C) in thousands of dollars on the amount of ore to extract from a copper mine measured in tons (T): 1) If you computed the average rate of change of cost with respect to tons for production levels between T = 20000 and T = 40000, give the units of your answer (no calculations - describe the units of the rate of change). 2) If you had a function for C(T) and were able to calculate the answer to part 1, explain why you would not expect your answer to be negative (explanation should be in terms of cost, tons of ore to extract, and rates of change).The production function is f (L, M ) = 5L1/2M 1/2, where L is the number of units of labor and M is the number of machines. If the amounts of both factors can be varied and if the cost of labor is $9 per unit and the cost of using machines is $64 per machine, then what is the total cost of producing 12 units of output?Given: Q = -0.0250 L3 + 1.5 L2 The chief economist for Argus Corporation, a large appliance manufacturer, estimated the firm’s short-run cost function for vacuum cleaners using an average variable cost function of the form AVC = a + bQ + cQ2 where AVC = dollars per vacuum cleaner and Q = number of vacuum cleaners produced each month. The total fixed cost each month is $180,000. The following results in the picture were obtained: a) Are the estimates ˆa, ˆb, and cˆ statistically significant at the 2 percent level of significance? Which is/are significant and which is/are not?b) Do the results indicate that the average variable cost curve is ∪-shaped? How do you know? c) If Argus Corporation produces 8,000 vacuum cleaners per month, what is the estimated average variable cost? Marginal cost? Total variable cost? Total cost? d) Answer part c, assuming that Argus produces 10,000 vacuum cleaners monthly. e) At what level of output will average variable cost be at a minimum? What is…
- Given the following cost functions: TC=100+60Q-3Q2+0.1Q3 TC=100+ 60Q+3Q2 TC=100 + 60Q In each case, indicate the point at which diminishing returns occurs. Also, indicate the point of maximum cost efficiency (i.e., the point of minimum average cost).(You will need to use a spreadsheet to tackle these questions.) 1. How much of q can be produced for £60,000 if the total cost function is TC = 86 + 152q − 12q2 + 0.6q3? 2. What output can be produced for £150,000 if TC = 130 + 62q − 3.5q2 + 0.15q3? 3. Solve for x when 0 = −1,340 + 14x + 2x2 − 1.5x3 + 0.2x4 + 0.005x5 − 0.0002x6The production function is f (L, M) = 5L1/2M1/2, where L is the number of units of labor and M is the number of machines. If the amounts of both factors can be varied and if the cost of labor is $9 per unit and the cost of using machines is $64 per machine, then the total cost of producing 12 units of output is a. $438. b. $108. c. $576. d. $115.20. e. $57.60.
- A small business woman has realized that for one of her products, if the price per unit is GH¢20 she can sell 300 units a day. On the other hand, if the price per unit is reduced to GH¢13, she can sell 440 units a day. From the accounting records, her accountant has estimated the fixed cost of production as GH₵2,000 with a variable cost per unit of GH¢10. (i). Find an expression relating price and output assuming it is linear. (ii). State the total cost function, assuming it is linear. (iii) Advise the business woman on the level of production at which she will breakeven.The total cost of manufacturing 360 units of a product is P6,620 and if 450 units are manufactured, the total cost will be P7,475. a) What is the variable cost per unit? b) What is the fixed cost? c) What is the average manufacturing cost for the first 360 units, for the 450 units, is it the same, Why? d) What is the total variable cost or 360 units? For 450 units, is it the same, why? e) What would be the selling price per unit if the desired profit per unit is 25%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?
