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- 1. For what value (s) of x is the function f(x) = 4/2x2 - 6x not continous? 2. If the demand of firm is QD (p) = 50 -3p and its supply function is Qs (p) = 14 + 6p. What is the equilibrium? 3. Find Lim x2 -4x + 3/55x−12/x^2−x−42 has vertical asymptote(s) at x=Consider the production function: Y = 0.75X + 0.0042X2 – 0.000023X3 At what level of X, the output will be maximum?
- How to find the the relative maximum or minmum of the function: e^(3x^2+4) with x and y coordinatesA company manufacturing laundry sinks has fixed costs of $100 per day but has total costs of $2,500 per day when producing 15 sinks. The company has a daily demand function of q = 360 − p, where q is the number if laundry sinks demanded and p is te price of a laundry sink. If production increases continuously, what is likely to be the average cost per sink?Find the number of units x that produces a maximum revenue R in the given equation.
- 1. The cost (in pesos) of producing x corkboards is given by x2 + 20x + 500, while the price (in pesos) of each corkboard if there is a demand for x units is given by p(x) = 100 − x.(a) Find the marginal profit of producing and selling 15 corkboards. (b) At what production level is the profit at a maximum?2. Due north, Seokjin is walking towards the most famous spot in a park at a rate of 1.3 meters per second. Due east, Yoongi is leaving the same spot at a rate of 1 meter per second. If they started walking at the same time, and Seokjin is initially 79 meters away from the spot, how fast is the distance between them changing after 30 seconds?The growth of bacteria in food products makes it necessary to time-date some products (such as milk) so that they will be sold and consumed before the bacteria count is too high. Suppose for a certain product that the number of bacteria present is given byƒ(t) = 500e0.1t,under certain storage conditions, where t is time in days after packing of the product and the value of ƒ(t) is in millions. (a) If the product cannot be safely eaten after the bacteria count reaches 3000 million, how long will this take?(b) If t = 0 corresponds to January 1, what date should be placed on the product?In the function: f(x)= (3x^2)ln(x) , x>0 What are the vertical asymptotes?
- Suppose a company has fixed costs of $54,400 and variable cost per unit of 4/9x + 222 dollars, where x is the total number of units produced. Suppose further that the selling price of its product is 1856 − 5/9x dollars per unit. (a) Find the break-even points (b) Find the maximum revenue. (c) Form the profit function P(x) from the cost and revenue functions.Lim as h approaches 0=[5e^x - 5e^(x+h)]/[3h]=In an economic enterprise, the total amount T that is produced is a function of the amount n of a given input used in the process of production. For example, the yield of a crop depends on the amount of fertilizer used, and the number of widgets manufactured depends on the number of workers. Because of the law of diminishing returns, a graph for T commonly has an inflection point followed by a maximum, so a cubic model may be appropriate. In this exercise we use the model shown below, with n measured in thousands of units of input and T measured in thousands of units of product. T = −2n3 + 3n2 + n (a) Make a graph of T as a function of n. Include values of n up to 1.5 thousand units. (b) Express using functional notation the amount produced if the input is 1.02 thousand units. (Round your answer to two decimal places.)T( )Calculate that value. (Round your answer to two decimal places.) thousand units(c) Find the approximate location of the inflection point. (Round…