1. Marginal revenue, cost, and profit. Let R(x), C(x), and P(x) be, respectively, the revenue, cost, and profit, in dollars, from the production and sale of x items. If: R(x) = 50x - 0.5x^2 and C(x) = 4x + 10
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- A company has two plants that produce the same lawn mower. If x1 and x2 are the numbers of units produced at plant 1 and plant 2, respectively, then the total revenue for the product is given by R = 300x1 + 300x2 − 5x21 − 10x1x2 − 5x22 . When x1 = 5 and x2 = 8, find (a) the marginal revenue for plant 1, ∂R/∂x1, and (b) the marginal revenue for plant 2, ∂R/∂x2.Suppose that the marginal-revenue function for a manufacturer's product is (dr/dq) = 100-(3/2)q2 , the marginal-cost function for a manufacturer's product is (dc/dq) = q2 -7q + 50, and the manufacturer has fixed costs of $5765. Find the profit function.Suppose that a company's average cost is A(x)=1.7x+7. Step 2 of 2: Determine the marginal cost.
- suppose that the price p of a product and its demand x are related through the price-demand equation x+400p=8000. Were interested to find all the values of p such that the demand is inelastic. which of the following gives the correct regionSuppose a company has fixed costs of $41,600 and variable cost per unit of 2/5x + 444 dollars, where x is the total number of units produced. Suppose further that the selling price of its product is 1776 − 3/5x dollars per unit. (a) Find the break-even points. (Enter your answers as a comma-separated list.) x = 1300, 32---correct (b) Find the maximum revenue. (Round your answer to the nearest cent.)$ 1314240----- correct(c) Form the profit function P(x) from the cost and revenue functions. P(x) = ????? Find maximum profit.$ 401956--- correct(d) What price will maximize the profit? (Round your answer to the nearest cent.)$ ??? only need help on c and dA company has found that the marginal cost (in thousands of dollars) to produce x central air conditioning units is C′(x)=30x3x2+e, where x is the number of units produced. (a) Find the cost function, given that the company incurs a fixed cost of $13,000 even if no units are built. (b) The company will seek a new source of investment income if the cost is more than $18,000 to produce 5 units. Should they seek this new source?
- Suppose a company has fixed costs of $46,800 and variable cost per unit of 2/5 x + 333 dollars, where x is the total number of units produced. Suppose further that the selling price of its product is 2159 − 3/5 x dollars per unit. Form the profit function P(x) from the cost and revenue functions. P(x) =Suppose that the monthly cost, in dollars, of producing x chairs is C(x)=0.004x3+0.07x2+15x+600, and currently 40 chairs are produced monthly. a) What is the current monthly cost? b) What is the marginal cost when x=40? c) Use the result from part (b) to estimate the monthly cost of increasing production to 42 chairs per month. d) What would be the actual additional monthly cost of increasing production to 42 chairs monthly?Given two inputs X1 and X2 with prices W1 and W2 respectively and a production function Y=f(X1,X2), show that cost minimisation implies that the marginal rate of substitution between the inputs X1 and X2 is equal to the ratio of the two inputs prices
- Suppose that the monthly cost, in dollars, of producing x chairs is C(x)=0.002x^3+0.07x^2+15x+600, and currently 90 chairs are produced monthly. a) What is the current monthly cost? b) What is the marginal cost when x=90? c) Use the result from part (b) to estimate the monthly cost of increasing production to 92chairs per month. d) What would be the actual additional monthly cost of increasing production to 92chairs monthly?Suppose that for a certain product the marginal cost is determined by means of C ^ '(x) = 1.02 (x + 200) ^ (0.02) and the marginal revenue by means of I ^' (x) = 2 / √ (4x + 1) +1.75, where x is in unit miles and income and cost are in dollar miles. Suppose further that fixed costs are 150 thousand dollars and that production is limited to a maximum of 200 thousand units. a) Find C (x) and I (x). b) Determine the level of production that gives maximum profit and find the maximum profit (or loss).Suppose the Marginal product of labor in the economy is given by MPN= .002(16,000-N), while the supply of labor is N=1000 + 1000w. Find the market clearing real wage rate and level of employment. What happens to the wage rate and employment if wealth rises, reducing the supply of labor to N= 500 + 1000w? As in (a), what is the unemployment rate if real wage is 1 more than the equilibrium wage? (hint: solve the real wage and then add it by 1, then find the difference of quantity of labor supplied and demanded).