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 МС- 4x+ 25, that its marginal revenue is MR%3D 75 - 6х, and that the cost of production of 60 units is $8,880. (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.
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- 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. 5000Cost, 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 = 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 $ .
- It costs a baker a fixed cost of $420 and variable cost of $2.10 per cupcake. A cupcake is sold for $4.90 each. (iv) Write an algebraic expression representing the revenue R as a function of the number of cupcakes x sold.(v) Graph both functions on the same coordinate axes.(vi) From your graph find coordinatae at which cost equals revenue.(vii) Using your graph, determine how many cupcakes need to be made to produce revenue of at least $1,029. How much profit is made for this number of cupcakes?It costs a baker a fixed cost of $420 and variable cost of $2.10 per cupcake. A cupcake issold for $4.90 each.(i) Make a table showing the total cost and the revenue obtained from producing 20,40,60,80 and 100 cupcakes.(ii) Write algebraic expressions representing the cost C and the revenue R as functions of the number of cupcakes X produced and number of cupcakes X sold respectively.(iii) Graph both functions on the same coordinate axes and from your graph determine the cordinate at which cost equals revenue.It costs a baker a fixed cost of $420 and variable cost of $2.10 per cupcake.A cupcake is sold for $4.90 each. (iv) Write an algebraic expression representing the revenue R as a function of the number of cupcakes x sold.
- A company finds that it can sell out a certain product that it produces, at the rate of Tk. 2 per unit. 1 It estimates the cost function of the product to be Tk. 1000 + 2 50 for q units produced. (i) Find the expression for the total profit, if q units are produced and sold. (ii) Find the number of units produced that will maximize profit. (iii)What is the amount of this maximum profit? (iv) What would be the profit if 6000 units were produced?For a certain product, suppose that total costs are given by c(x) = 1600 + 1500x and total revenues by R(x) = 1600x-x2 (b) Find the profit function, p(x). c) Find the number of units that will maximize profit. (d) Find the maximum profit.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 $ .
- Assume that it costs a company approximately C(x) = 400,000 + 140x + 0.003x? dollars to manufacture x smartphones in an hour. (a) Find the marginal cost function. 400,000 – 0.000009 Use it to estimate how fast the cost is increasing when x = 10,000. 2$ per smartphone Compare this with the exact cost of producing the 10,001st smartphone. The cost is increasing at a rate of $ per smartphone. The exact cost of producing the 10,001st smartphone is $ Thus, there is a difference of $ (b) Find the average cost function C and the average cost to produce the first 10,000 smartphones. C(x) = C(10,000) = $ (c) Using your answers to parts (a) and (b), determine whether the average cost is rising or falling at a production level of 10,000 smartphones. -Select--- at a production level of 10,000 smartphones. The marginal cost from (a) is --Select--- than the average cost from (b). This means that the average cost isA 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?The total cost and the total revenue (in dollars) for the production and sale of x ski jackets are given by C(x)=26x +18,625 and R(x)-200x-0.2x² for 0≤x≤ 1000. (A) Find the value of x where the graph of R(x) has a horizontal tangent line (B) Find the profit function P(x). (C) Find the value of x where the graph of P(x) has a horizontal tangent line. (D) Graph C(x), R(x), and P(x) on the same coordinate system for 0sxs 1000. Find the break-even points. Find the x-intercepts of the graph of P(x) (A) R(x) has a horizontal tangent line at x =