2. If the price/demand function is p-50-1.25x and the total cost function is 160+10x, where x is the number of units (D) in thousands and cost is in dollars, determine the following: a. General Equation of the Total Profit (profit function) b. General Equation of the Total Revenue (revenue function)
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- 3. Suppose that the total revenue function for a commod- ity is R = 64x- 0.02x². (a) Find R(100) and tell what it represents. (b) Find the marginal revenue function. (c) Find the marginal revenue at x = 100 and tell what it predicts about the sale of the next unit and the next 3 units. (d) Find R(101) - R(100) and explain what this value represents.The figure shows graphs of the total cost function and the total revenue function for a commodity. (Assume cost and revenue are measured in dollars.) y 500 400 300 200 100 MR 10 (a) Label each function correctly. function A ---Select--- function B ---Select--- (x, y): = 20 (b) Determine the fixed costs. $ 30 (c) Locate the break-even point. -([ = 40 50 Determine the number of units sold to break even. units A B 60 (d) Estimate the marginal cost MC and marginal revenue MR. MC = X2. If the price/demand function is p-50-1.25x and the total cost function is 160+10x, where x is the number of units (D) in thousands and cost is in dollars, determine the following; a. General Equation of the Total Profit (profit function) b. General Equation of the Total Revenue (revenue function) C. Breakeven points
- 4. Find the optimum values. (i) Find the minimum value of Q that minimize the cost function: C= 30²-70+ 12. (ii)Find the maximum value of Q that maximize the revenue function: R = 100-Q².7. A paint store sells 270 pails of paint per month at a price of $32 each. A customersurvey indicates that for each $1.20 decrease in price, sales will increase by 6pails of paint.(a) Determine the demand, or price, function.(b) Determine the revenue function (using (a)).(c) Determine the marginal revenue function.(d) Solve R’(x) = 0. Interpret the meaning of this value for this situation.(e) What is the price that corresponds to the value found in part (d)?Calculate Total revenue if average revenue is $15 and output is 1000
- need d and e rest part are solved answer is here Solution:- Given Monthly demand function: Q=300-4P .... (1) Cost function: TC=15Q+1000 ..... (2) Part a Revenue = Price * quantity Q=300-4P⇒4P=300-Q⇒P=75-0.25Q So R=PQR=75-0.25QQR=75Q-0.25Q2 ... (3) To maximize revenue, differentiate the equation 3 with respect to Q dRdQ=75-0.5Q Put dRdQ=075-0.5Q=0⇒0.5Q=75⇒Q=150 Second-order condition for revenue maximization: d2RdQ2=-0.5<0 Revenue is maximization quantity is 150 From equation 3 R=75×150-0.25×1502R=5625 The maximum revenue is $5625 part b Differentiate equation 1 with respect to Q dQdP=-4 Price elasticity is calculated as e=dQdP×PQe=-4×75-0.25×150150e=-4×0.25e=-1 Price elasticity at revenue-maximizing point is -1 part c Total cost of producing 150 units: TC=15×150+1000TC=3250 Profit at revenue-maximizing level of output: Profit = revenue - costProfit =5625-3250Profit =2375A local newspaper currently has 84,000 subscribers at a quarterly charge of $30.Market research has suggested that if the owners raise the price to $32, they wouldlose 5,000 subscribers. Assuming that subscriptions are linearly related to theprice, what price should the newspaper charge for a quarterly subscription tomaximize their revenue?a) Find the cost function (Hint: find slope and use point-slope form to find thecost function) b) Find the revenue function c) Find the maximum revenue d) Find the profit functionA donut shp has a fixed cost of $92000 per day and a varibale cost of $2 for each donut produced. If the donuts are sold to distributors for $5 each. What is the price-demand function? What is the revenue function?
- A firm in a perfectly competitive industry has fixed costs of FC = 15, marginal costs of MC = 5 + 14q, and average variable costs of AVC = 5 + 7q. (a) What are the firm’s variable costs (VC)? (b) What is the firm’s total cost function? (c) If the price is $75, how much does the firm supply? (d) Does the firm continue to supply this quantity in the short-run? (e) Suppose there exists a standard market demand function from consumers (downward slopping). Please provide a logical discussion about how the market achieves short-run equilibrium.Given cost and price (demand) functions C(q) = 100q + 41,000 and p(q) = - 2q + 890, what price maximizes revenue? My Co It would be $ per item. Cours (Round answer to two decimal places.) Anno Calen CullThe following graph illustrates the weekly demand curve for motorized scooters in Roanoke. Use the green rectangle (triangle symbols) to compute total revenue at various prices along the demand curve. Note: You will not be graded on any changes made to this graph. PRICE (Dollars per scooter) 260 240 220 200 180 160 140 120 100 80 60 40 20 0 0 9 18 27 A X B Demand 36 45 54 63 72 81 QUANTITY (Scooters) 90 99 108 117 Total Revenue ?