A firm knows that its marginal cost for a product is MC = 4x + 20, that its marginal revenue is MR = 50 – 6x, and that the cost of production of 100 units is $22,100. (a) Find the optimal level of production. units (b) Find the profit function. P(x) = (c) Find the profit or loss at the optimal level. There is a profit v of $
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- Cost, revenue, and profit are in dollars and x is the number of units. A firm knows that its marginal cost for a product is MC = 2x + 25, that its marginal revenue is MR = 73 – 6x, and that the cost of production of 80 units is $8,560. (a) Find the optimal level of production. units (b) Find the profit function. P(x) = (c) Find the profit or loss at the optimal level. There is a -Select--- v of $Cost, revenue, and profit are in dollars and x is the number of units. A firm knows that its marginal cost for a product is MC = 3x + 30, that its marginal revenue is MR = 62 − 5x, and that the cost of production of 60 units is $7,300. (a) Find the optimal level of production. units (b) Find the profit function. P(x) = (c) Find the profit or loss at the optimal level. There is a ---Select--- profit loss of $ .Cost, revenue, and profit are in dollars and x is the number of units.A firm knows that its marginal cost for a product is MC = 2x + 25, that its marginal revenue is MR = 43 − 4x, and that the cost of production of 80 units is $8,560. (a) Find the optimal level of production. units(b) Find the profit function. P(x) = (c) Find the profit or loss at the optimal level. There is a ---Select--- profit loss of $ .
- 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.)Cost, revenue, and profit are in dollars and x is the number of units. A firm knows that its marginal cost for a product is MC = 2x + 20, that its marginal revenue is MR = 44 − 6x, and that the cost of production of 100 units is $12,160. the optimal level of production is 3 units. a) find the profit function b) Find the profit or loss at the optimal level.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. 5000
- When the admission price for a baseball game was $4 per ticket, 50,000 tickets were sold. When the price was raised to $5, only 45,000 tickets were sold. Assume that the demand function is linear and that the variable and fixed costs for the ball park owners are $0.10 and $95,000 respectively. (a) Find the profit P as a function of x, the number of tickets sold. P(x) = (b) Select the graph of P. y 150000 y 150000 150 000 100 000 100 000 100 000 50 000 50 000 50 000 20000 40 000 60 00p 20000 40 000 60 000 20000 40 000 60 000 - 50 000 -50 000 -50 000 -100 000 100000 100000 The xy-coordinate plane is given. The curve starts at the approximate point (0, 3,000), goes up and right becoming less steep, and exits the window at the approximate point o-150000 O o-150000L O O (70,000, 69,000). 150000 100 000. 50 000- 20000 40 000 60 do0 - 50 000 100 000- o 150 000The profit of a company, in dollars, is the difference between the company's revenue and cost. The cost, C(x), and revenue, R(x), are functions for a particular company. The x represents the number of items produced and sold to distributors. C(x)=-2300+40x R(x)=840x-x² a) Determine and simplify the profit function. Write your answer in descending order. P(X)-As a production process requires labor L and capital K, q = F (L, K). The wage for a labor is $500, the cost for one capital is $250. If the firm has a budget of $7500 to produce, what is the firm's optimum output 250 200 100 150
- To produce the next popular toy, a company has to pay a factory $250, 000 to set up the production line. They also have to pay $25 per item for the raw materials and labor. Write function for the average cost to produce x items. Then describe what happens to the average cost as the factory produces a large number of toys.The total cost and the total revenue (in dollars) for the production and sale of x ski jackets are given by C(x) = 28x + 20,160 and R(x) = 200x - 0.2x2 for 0sxs 1000. Find the value of x where the graph of R(x) has a horizontal tangent line. Find the profit function P(x). Find the value of x where the graph of P(x) has a horizontal tangent line. Graph C(x), R(x), and P(x) on the same coordinate system for 0 sxs 1000. Find the break-even points. Find the x-intercepts of the graph of P(x).The market for high-quality caviar is dependent on the weather. If the weather is good, there are many fancy parties and caviar sells for 300 SEK per kg. In bad weather it sells for only 200 SEK per kg. Caviar produced one week will not keep until the next week, i.e. it has to be sold and consumed the same week it is produced. A small caviar producer has a cost function given by C=5q2 - 50q + 1000 where q is the weekly caviar production. Production decisions must be made before the weather (and hence the price of caviar) is known, but it is known that good weather and bad weather each occur with a probability of 0.5. a) How much caviar should the firm produce per week if it wishes to maximise its expected profit? b) Suppose the owner of the firm has a utility function of the form U(π)=√π where π is weekly profits. What is the expected utility associated with the strategy in (a)? c) Suggest a weekly production level that would give the owner higher expected utility than the…