A two product firm faces the following demand and cost functions: Q1 = 40 - 2P1 - P2 Q2= 35 - P1 - P2 C = Q21 + 2 Q22 + 10 (a) Find the output levels that satisfy the first-order condition for maximum profit. (use fractions.) (b) Check the second-order sufficient condition. Can you conclude that this problem possesses a unique absolute maximum? (c) What is the maximal profit?
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A two product firm faces the following demand and cost functions:
Q1 = 40 - 2P1 - P2 Q2= 35 - P1 - P2 C = Q21 + 2 Q22 + 10
(a) Find the output levels that satisfy the first-order condition for maximum profit. (use fractions.)
(b) Check the second-order sufficient condition. Can you conclude that this problem possesses a unique absolute maximum?
(c) What is the maximal profit?
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- A 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. (d) How many laundry sinks will the company need to produce in order to maximise it′s profits?A 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. (e) What is the maximum profit?A firm will break even (no profit and no loss) as long as revenue just equals cost. The value of x (the number of items produced and sold) where C(x) = R(x) is called the break-even point. Assume that the below table can be expressed as a linear function. Find (a) the cost function, (b) the revenue function, and (c) the profit function. (d) Find the break-even point and decide whether the product should be produced, given the restrictions on sales. Fixed cost Variable cost Price of item $15 $300 $30 According to the restriction, no more than 17 units can be sold. (a) The cost function is C(x) =. (Simplify your answer.)
- A two - product firm faces the following demand and cost functions: Q1 = 40 - 2P1 - P2 Q2 = 35 - P1 - P2 C = Q 2/1 + 2Q 2/2 + 10 (a) find the output levels that satisfy the first order condition for maximum profit. (use fractions) (b) check the second - order sufficient condition. Can you conclude that this problem possesses a unique absolute maximum? (c) What is the maximal profit?2) The owner of a restaurant that you are thinking of purchasing, tells you for x customers per week the weekly cost and revenue in dollars is C(x) = 15000+2x and R(x) = 500x-3x² a) Find the profit function P(x) b) Find the break-even quantities rounding properly to a whole number. (Hint: Use the Quadratic formula) c) Why is the minimum break-even quantity important?The demand function and total cost function for a product are 6P = 660 − 3Q, TC = 80 − 20Q2 + 600Q (a) Write down expressions for: (i) average cost, (ii) marginal cost, (iii) total revenue, (iv) marginal revenue, (v) profit. (b) Determine the values of Q for which total cost is a maximum. Calculate the maximum costs. Calculate the profit when total costs are a maximum. (c) Determine the value of Q for which profit is a minimum. What is the minimum profit?
- Consider a firm with the market demand function for its product given by: p =1000 – 2Q; and total cost of production given by: TC = Q3 – 59Q2 + 1315Q + 2000. (a) Obtain the firm’s Total Revenue function. (b) Find the amount of Total Revenue when the firm sells 30 units of output. (c) Obtain the firm’s Profit function. (d) Find the amount of Total Profit when the firm sells 30 units of output.A firm faces the demand schedule p = 190 – 0.6q TC = 40 + 30q + 0.4q. %3D and the total cost function %3D (a) What output will maximize profit? (b) What output will maximize total revenue? (c) What will the output be if the firm makes a profit of £4,760?Given Cost and Price (demand) functions C(q) = 110q + 45000 and p(q) = - 2.8q + 800, what profit can be earned if the price is set to be $550 per item? U The profit is $ 1,?9 (Round to the nearest cent.) A company produces a special new type of TV. The company has fixed costs of $499,000, and it costs STT00 to produce each TV. The company projects that if it charges a price of $2300 for the TV, it will be able to sell 850 TVs. If the company wants to sell 900 TVs, however, it must lower the price to $2000. Assumo a linear demand. What is the marginal profit if 200 TVs are produced It is $ 0 per item. (Round answer to nearest dollar.)
- X If total revenue received from the sale of x items is given by R(x) = 10 In (4x + 1), while the total cost to produce x items is C(x) = ¹ (a) The marginal revenue (b) The profit function P(x) (c) The marginal profit when x = 40 (d) Interpret the results of part (c). (a) How can the marginal revenue be found? A. Find R(x) - C(x). B. Find the derivative of R(x). C. Find the derivative of R(x) - C(x). R( 2 ). D. Find R find the following.The total Revenue curve of a firm is R(q) = 40q -12q^2 and its average cost A(q) = 1/30q^2 – 12.85q + 20 + 400/q, where q is the firm’s output. (i) Derive an expression C(q) for the firm’s total cost function. (ii) Derive an expression for the firm’s profit function. (iii) Is the rate of change of profit increasing or decreasing when the output level of the firm is 10 units? (iv) Determine the level of output for which the firm's profit is maximized (v) What is the firm’s maximum profit?A firm uses the production technology q = (x{ + xP, where a is a constant and 0 # p< 1. (a) Derive the firm's cost function, c(w1,W2,9). (b) Derive the firm's profit, 7(p,w1,w2). (c) Derive the elasticity of scale for this production technology. (d) What restrictions must a satisfy to ensure that the profit function is well-defined? Explain.