The supply function for a product is given by p = 40 + 100V2x + 4, where x is the number of units supplied and p is the price in dollars. If the price is increasing at a rate of $1 per month, at what rate (units/month) is the supply changing when the price per unit is $840? units/month
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- Worldwide annual sales of a device in 2012–2013 were approximately q = −6p + 3,040 million units at a selling price of $p per unit. Assume a manufacturing cost of $40 per unit. [HINT: Recall that Profit = Revenue − Cost.] Find the function P for annual profit, in millions of dollars and in terms of p only, subject to any constraints. P(p) = ____ Find P′(p). P′(p) = ____ What selling price (in dollars) would have resulted in the largest annual profit? (Round your answer to two decimal places.) p = $____ What would have been the resulting annual profit (in millions of dollars)? (Round your answer to the nearest whole number.) $ ____ millionIf the transit time is 11 days and the annual demand for an item is 10,000 units, whatis the average annual inventory in transit?The profit function in dollars for a product is given -x^3+76x^2-380x-2800 where x is the number of units produced and sold. If break even occurs when 10 units are produced and sold find a quadratic factor of the profit function and find a number of units other than 10 that gives break even for the product.
- The growth rate of the demand for coal in the world is 6 % per year. In what year will the demand be double that of 1997 ? Note:- Please avoid using ChatGPT and refrain from providing handwritten solutions; otherwise, I will definitely give a downvote. Also, be mindful of plagiarism. Answer completely and accurate answer. Rest assured, you will receive an upvote if the answer is accurate.An apple grower has discovered a process for producing oranges that requires two inputs. The production function is Q = min{2x, y}, where x and y are the amounts of inputs 1 and 2 that he uses. The prices of these two inputs are wx = $5 and wy = $10, respectively. The minimum cost of producing 160 units is therefore:a. $2,400.b. $1,600c. $800.d. $2,000.e. $8,000. Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You will get up vote for sure.The consumption of electricity in one area has increased historically at 6% per year.If it continues to increase at this rate indefinitely.Find the the number of years before the electricity utility would need to double the amount of generation capacity
- Manning Inc. is the leading manufacturer of garage doors. Demand for residential garage doors depends, of course, on the rate at which new houses are being built, which in turn depends on changes in income per capita. During the past year, Manning sold 10 000 garage doors at an average price of R1 500 per door. In the coming year, disposable income per capita is expected to increase from R32 000 to R34 000. Without any price change, Manning expects current-year sales to rise to 12 000 units. 1. Calculate the arc income elasticity of demand. 2. The company economist estimates that in conjunction with the change in income, if the price of doors is increased by R100, they could sell 11 500 doors. What is the arc price elasticity and what would be the company’s revenue? 3. Should they raise the price even more?The output (Q) of a production process is a function of two inputs (L and K) and K is given by the following relationship: Q = 0.50LK− 0.10L2− 0.05K2 The per-unit prices of inputs L and K are $20 and $25, respectively. The firm is interested in maximizing output subject to a cost constraint of $500. Use the lagrangian optimization techniques to find the following: How many units of L and K should be used by the firm? What is the total output of this combination? What is the marginal rate of substitution between L and K?The demand equation for a product for a product brand of mackerel is given by the equation Qx=50-7Px+0.002I+12Py Where Qx=monthly consumption per family in cartons Px=price per carton of makerel=GHC 2.00 I=median annual family income=GHC20,000 Py=price per carton of competing brand of mackerel=2.5 Required: i.At the stated values of the explanatory variables,calculate the consumption of makerel(cartons). ii.what is the relationship between Good x and Good y? iii.what is the nature of Good x ? iv.Suppose the median annual family income increases to GHC40,000,What will be your new consumptino for Good x? v.Suppose that the price per carton of competing brand increases GHC3.00, What will be your new consumption for Good x?
- 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?analysis of the data indicated that the demand curve for x product is estimated to be linear and given by equation Qd = 150-3P and the supply curve for x product appears to be linear as well and is estimated as Qs=P-10. Graphically draw these two curves, labeling all relevant looking (such as intercepts for each line) on the horizontal and vertical axesIt is known that a certain company sells each kg of the product it manufactures at $80, it is also known that the total manufacturing cost "CT" is given by the function CT=(1/1000)x2 +100 , where "x" are the kg of product produced. a) How many units of "x" must the company sell to break even? Value = 100 points.b) How many units of "x" is the optimal quantity that should be sold to optimize the producer's profit? Value = 100 points.c) How many monetary units does that optimal profit for producers amount to? (remember, you will have to prove it mathematically either by the method of the first or by the method of the second derivative). Value = 100 points.