The demand for a particular item is given by the function D(x)=1500-3X^2. find the consumers surplus if the equilibrium price of the unit is $300
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- How are the absolute maximum and minimum similar to and different from the local extrema?The demand function for device model ADN781 is given by p(x)=510−0.18x2, where pp is the unit price (in dollars) and xx is the quantity demanded (in thousands of units).If adverse conditions are driving the price up by $5 per week, find the rate at which the quantity demanded for device model ADN781 is changing when the price is $438.The cost per unit of producing a product is 280 + 0.2x dollars, where x represents the number of units produced per week. If the equilibrium price determined by a competitive market is $420, how many units should the firm produce and sell each week to maximize its profit? unit
- How many units of special lamp and the regular lamp should be produced per production period in order to maximize the the profit ?The price elasticity of supply for bananas is 0.2. If the price rises by 5%, what will happen to the quantity supplied? What would this elasticity imply about seller's production capacity?A small business invests $25,000 in a new prod- uct. In addition, the product will cost $0.75 per unit to produce. Find the cost function and the average cost function. What is the limit of the average cost function as production increases?
- Suppose a product has a daily marginal revenue of 46 dollars per unit, and a daily marginal cost of 30 + 1/2x dollars per unit. If the daily fixed cost is $200, how many units will give a maximum profit, and what is the maximum profit?A firm in a competitive market must sell its product for $250 per unit. The cost unit (per month) is 50 + 2x ,where x represents the number of units sold per month. Find the marginal profit function if the production levels is 5 units.As with discrete-time dynamical systems, equilibria can act strange when the slope of the rate-of-change function is exactly equal to the critical value of zero. Graph a rate-of-change function that has a slope of 0 at the equilibrium but the equilibrium is stable. What is the sign of the second derivative at the equilibrium? What is the sign of the third derivative at the equilibrium?
