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,
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Q3) 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?
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- 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?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 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?
- 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.A company produces very unusual CD's for which the variable cost is $ 15 per CD and the fixed costs are $ 50000. They will sell the CD's for $ 79 each. Let a be the number of CD's produced. Write the total cost C as a function of the number of CD's produced. C =$ Write the total revenue R as a function of the number of CD's produced. R=$ Write the total profit P as a function of the number of CD's produced. P=$ Find the number of CD's which must be produced to break even. The number of CD's which must be produced to break even is Question Help: Video Submit QuestionA 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.)
- Central Grocery in New Orleans is famous for its muffaletta, a large round sandwich filled with deli meats and topped with a tangy olive salad. Suppose the following table represents cost and revenue data for Central Grocery. Muffaletta Sold per Day Price (P) Total Revenue (TR) Marginal Revenue (MR) Total Cost (TC) Marginal Cost (MC) Average Total Cost (ATC) Profit 0 $15 $12 1 14 18 2 13 20 3 12 21 4 11 23 5 10 26 6 9 30 7 8 35 8 7 42 9 6 52 10 5 78 Fill in the table What are the profit-maximizing price and quantity, and what…= Suppose that the marginal revenue for firefighting protective clothes is MR marginal cost is MC = 3.5x + 15 with a fixed cost of $295. Assume R(0) = 0. a) How many units will result in a maximum profit? x = b) Find the revenue function. R(x) c) Find the cost function. C(x) 337.5 4x and the d) What is the maximum profit (to the nearest dollar)? The maximum profit isA 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. (b) Find a function for the average cost of this company?
- (3) 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. a) If we assume that the total cost per day is linearly related to the amount of sinks produced in a day, derive the total cost function of the company? b) Find a function for the average cost of this company.Эшestion 1 A computer retailing company specializes in the sale of jump drives to community college tudents. The demand function for jump drives is p=2x+10x+1000 dollars For the samne company the average cost function is given as: ē = 2x +36x-1600- 20 * dollars Where p is the price in dollars and x represents units of output. 1) i1) Find the price and output that will maximize profit. Find the maximum profitGiven 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.)
