Suppose a company's revenue function is given by R(q)=−q^3+360q^2 and its cost function is given by...

Suppose a company's revenue function is given by R(q)=−q^3+360q^2 and its cost function is given by C(q)=300+19q where q is hundreds of units sold/produced, while R(q) and C(q) are in total dollars of revenue and cost, respectively.

A) Find a simplified expression for the marginal profit function. (Be sure to use the proper variable in your answer.)

MP(q)=

B) How many items (in hundreds) need to be sold to maximize profits? (Round your answer to two decimal places.)

Answer: hundred units must be sold.

Solutions

Expert Solution

milcah answered 1 year ago

Next > < Previous

Related Solutions

Suppose a company's revenue function is given by R(q)=−q3+320q2R(q)=-q3+320q2 and its cost function is given by...

Suppose a company's revenue function is given by R(q)=−q3+320q2R(q)=-q3+320q2 and its cost function is given by C(q)=290+20qC(q)=290+20q, where qq is hundreds of units sold/produced, while R(q)R(q) and C(q)C(q) are in total dollars of revenue and cost, respectively. A) Find a simplified expression for the marginal profit function. (Be sure to use the proper variable in your answer.) MP(q)=MP(q)= B) How many items (in hundreds) need to be sold to maximize profits? (Round your answer to two decimal places.)

Suppose that the cost of producing q appliances is c(q)=200-q+0.96q^2 and the demand function is given...

Suppose that the cost of producing q appliances is c(q)=200-q+0.96q^2 and the demand function is given by q=400-25p. Develop the total revenue, total cost (if not given), and profit functions. Explain these functions in few sentences. Compute the point elasticity of demand. Find the intervals where the demand is inelastic, elastic, and the price for which the demand is unit elastic. Find the quantity that maximizes the total revenue and the corresponding price. Interpret your result. Find the quantity that...

A production function is given by q = L1/3K1/3 and a total cost function is given...

A production function is given by q = L1/3K1/3 and a total cost function is given by TC = q2/3. Under what conditions could these belong to the same firm?

Suppose that a price-setting firm has the following total revenue and total cost functions: R(q) =...

Suppose that a price-setting firm has the following total revenue and total cost functions: R(q) = 10.75q – 0.1875q2 and C(q) = 75 + 0.07q + 0.035q2 . This firm faces downward sloping demand and marginal revenue curves. Marginal revenue and marginal cost are given by ?? ?? = ??(?) = 10.75 – 0.375? and ?? ?? = ??(?) = 0.07 + 0.07?, respectively. a. Using the marginal revenue function given above, find an expression for the firm’s demand curve...

2. Given a firm's demand function Q-90+2P=0 and its average cost function AC= Q2-39.5Q+120+(125/Q) find the...

2. Given a firm's demand function Q-90+2P=0 and its average cost function AC= Q2-39.5Q+120+(125/Q) find the level of output (Q) which a) Maximizes Total Revenue b) Minimizes Marginal Cost c) Maximizes Profits. 3. A monopolistic firm has the following demand functions for each of its products X and Y: X=72-0.5Px Y=120-Py The combined cost function is C=X2+XY+Y+35. The maximum production capacity is 40 and given by X+Y=40. Find the profit maximizing levels of output, prices and profit.

2. Suppose that a firm's production function is given by Q = KL(MPK = L and...

2. Suppose that a firm's production function is given by Q = KL(MPK = L and MPL = K), where Q is the quantity of output, K is units of capital, and L is units of labor. The price per unit of labor and capital are $30 and $20, respectively. (a) How many units of labor and capital should the firm use if it wants to minimize the cost of producing 600 units of output? (b) Suppose that the firm...

1. Suppose that a competitive firm’s marginal cost function is given by MC(q) = 4 +...

1. Suppose that a competitive firm’s marginal cost function is given by MC(q) = 4 + aq, where a > 0 and the market price is 16. a) What is the firm’s profit-maximizing level of output when a = 4? b) Suppose the firm’s fixed costs increase and the value of a decreases. How will this affect the firm’s profit-maximizing level of output? c) Suppose the firm’s producer surplus at its profit-maximizing level of output is 36. What is the...

Suppose that the inverse demand function for a monopolist's product is: p=7-(Q/20) Its cost function is:...

Suppose that the inverse demand function for a monopolist's product is: p=7-(Q/20) Its cost function is: C=10+14Q-4Q^2+(2Q^3/3) Marginal revenue equals marginal cost when output equals: q=_ units and q=_units (Enter numeric responses using real numbers rounded to three decimalplaces.) What is the profit maximizing output?

A production function is given by q = L1/5K1/5 and a total cost function is given...

A production function is given by q = L1/5K1/5 and a total cost function is given by TC = q2/5. Under what conditions could these belong to the same firm?

Profit = Revenue - Cost P(x) = R(x) - C(x) Given: R(x) = x^2 - 30x...

Profit = Revenue - Cost P(x) = R(x) - C(x) Given: R(x) = x^2 - 30x Given: C(x) = 5x + 100 X is hundreds of items sold / P, R, C are in hundreds of dollars (1) Determine the Initial Cost? (2) Determine the maximum Profit and number of items required for that profit? (3) Determine the maximum Revenue and number of items required for that revenue? (4) Find the break even points, P(x) = 0. What do the...

Subjects