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A firm has the following benefits and costs equations: B(Q) = 450Q - 26Q² and MC(Q) = 136Q
The Q that maximum total benefit = ?
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- A firm has the following benefits and costs equations: B(Q) = 450Q - 26Q² and MC(Q) = 136Q Q that max NB? The maximum net benefit is (profits)?A firm's production function is given by Q = 40K0.8L0.2 Each unit of capital costs $40 and each unit of labour costs $80. (a) Find the maximum level of output if the total input costs are $400,000. (b) Estimate the increase in production if an addtional $5,000 is made available. (c) Show that the ratio of marginal product to price is the same for both inputs. (a) Maximum output Q = (Round to the nearest integer as needed.) (b) Increase in output is units (Round to the nearest unit as needed.) (c) The ratio of the marginal product of capital to price is (Round your answer to two decimal places.) The ratio of the marginal product of labour to price is (Round your answer to two decimal places.)C(x) = 0.01x-0.3x + 10x gives the cost, in thousands of dollars, to produce x thousand items. (a) Find a formula for the marginal cost. (b) Find C'(0). Give units. (c) Graph the marginal cost function. Use your graph to find the minimum marginal cost, the production level for which the marginal cost is the smallest. (d) For what value of x does the marginal cost return to C'(0)? (a) Find a formula for the marginal cost. c'(x) =D (b) Find C'(0). Give units. c'(0) = (c) Use the derivative of the marginal cost function to find the minimum marginal cost, the production level for which the marginal cost is the smallest. The minimum marginal cost of additional dollars per item produced occurs when thousand items are produced. d) Recall your answer to part b. For what value of x does the marginal cost return to C'(0)? Marginal cost returns to this value of C (x) when x = items are produced.
- Crawford Computing finds that its weekly profit, in dollars, from its production and sale of x laptop computers is P(x)=-.002x^3-.15x^2+400x-800 Currently, Crawford builds and sells 9 laptops weekly. (a) what is the current weekly profit? (b) how much profit would be lost if production and sales dropped to 8 laptops weekly? (c) what is the marginal profit with x=9? (d) use answers from parts (a) and (c) to estimate the profit resulting from the production and sale of 10 laptops weekly.(b) A firm has an average cost function A(q) = 125 q + q 2 16 − 4. where q is the firm′ s output. (i) Determine the level of output for average costs are minimum. (ii) Hence determine the range of values for which average costs are decreasing. (iii) What part of the decreasing range is practically feasible? (iv) Write an equation for the total cost function. (v) Hence calculate the level of output for which total costs are minimum. Can I get the answer for (iv) and (v) please(a) How would one estimate the full cost to an airline if one of its planes is held over for 24 hours in an airport for repair? (b) A company has spent $10 million to develop a product for market. During the product’s first two years, the company’s profit was $6 million. In recent years, the market was flooded by rival products and now the company is reassessing its product. If it abandons the product, it can recover $2 million of its original investment by selling its production facility. If it continues to produce the product, its estimated revenues for successive two-year periods will be $5 million and $3 million and its costs will be $4 million and $2.5 million. (After four years the plant will have zero resale value.) What would be the company’s best course of action? (c) Two decades ago, the global demand and supply curves for copper were: Qd = 15-10P and Qs = -3 + 14P, where Q is measured in millions of metric tons per year. Find the competitive price and quantity. Suppose that…
- When x gallons of olive oil are produced, the profit function is given by P(x) = 2x – 1000 (i) Find the value of x that maximizes profit. (ii) Compute maximum profit. 5000How do you find the marginal costs (questions d and e)As a producer and seller of some commodity, you have learned that, if you produce and sell x itmes in a particular month, the following functions can be used to find the cost and revenue: Revenue: R(x)=150x-x^2 and Cost: C(x)=3000+20x. (a) Write a simplified formula for your profit in a particular month, P(x)=R(x)- C(x) (b) Find the "break-even" point(s) (c) How many items should you produce and sell in a month in order to achieve a maximum profit? (d) What is the maximum possible monthly profit? This is the problem and I cannot solve the c and d, could you please help me?
- A shop which sells T-shirts has a demand function and a total cost function given by the equations P = 240 − 10Q and TC = 120 + 8Q (a) Write down the equations for TR and profit. (b) Calculate the number of T-shirts which must be sold to maximize (i) profit, (ii) total revenue. (c) Write down the equations for MR and MC.A firm uses a single input to produce a commodity according to itsshort-run production function f(x) = 4√x, where x is the number of units ofinput. The commodity sells for $100 per unit. The input cost $50 per unit.(a) Write down a function that states the firm’s profit as a function ofthe amount of input.(b) What is the profit maximizing amount of input and output?(c) Suppose the firm is taxed $20 per unit of its output and the priceof its input is subsidized by $10, explain in detail how this will affect the newinput and output levels?which quote best represents a person performing a cost-benfit analysis?