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A startup software company has indicated its cost, c(x), and revenue, f(x), as given below, such that x is the number of lines of programing code (units in 1000 lines).
c(x) = 80000 - 2(x-200)2
f(x) = (x-10)3 + (x+10)2
- Find the marginal cost analytically, and draw its graph
- Find the marginal revenue analytically, and draw its graph
- Solve for the x point where marginal cost is equal to marginal revenue analytically. Comment why is this point significant analytically.
- Write the profit function and draw its graph
- Is the profit function concave up or concave down?
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- It costs a baker a fixed cost of $420 and a variable cost of $2.10 per cupcake. A cupcake is sold for $4.90 each. (i) Make a table showing the cost of producing 20,40,60,80 and 100 cupcakes. (ii) Make a table showing the revenue from selling 20,40,60,80 and 100 cupcakes. (iii) Write an algebraic expression representing the cost C as a function of the number of cupcakes x that are produced. (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 coordinates 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?The''Sad Student'' Company finds that it costs a total of (q)=9720+500q-1.5q^(2)+0.005q^(3) Dollars to produce q lots of its latest board game named ''Calculus Teacher Shooter'' each lot of 100 games. A)Analyze the behavior of cost function. B)Interpret the constant term in the expression C C)Analyze the behavior of the marginal cost as a function of the output q. D)Interpret the effect of the constant term in the expression of total cost function on marginal cost function. E)Analyze the behavior average cost funtion. F)Analyze interaction of marginal cost and average cost numerically; and derive the formula of this relationship with respect to relevant mathematical economics theory and interpret your formula.= 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 is
- The cost, in thousands of dollars, of airing x television commercials during a sports event is given by C(x) = 150 + 2,600x – 0.06x2. (a) Find the marginal cost function C'(x). C'(x) = (b) Use the marginal cost to approximate the cost to air the 5th commercial. Convert your answer to dollars. The cost to air the 5th commercial is approximately X dollars. (c) What is the exact cost to air the 5th commercial? Convert your answer to dollars. The exact cost to air the 5th commercial is x dollars.Fill in the appropriate numbers in the blank spaces, given the following information:output Total fixedcost (RM) Totalvariable cost(RM) Averagefixedcost(RM)Averagetotal cost(RM)Marginalcost(RM) 0 100 01 100 202 100 503 100 604 100 655 100 70To 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.
- Given the total cost function TC = 100 + 40Q - 15Q2 + 5Q3, what is Average Total Cost (ATC)? A. ATC = 40 – 15Q + 5Q2 - B.ATC = 40 – 30Q + 15Q2 C.ATC = 100/Q + 40 – 15Q + 5Q2 D.ATC = 10 + 4Q – 1.5Q2 + 0.5Q311.2 The cost, in thousands of dollars, of airing x television commercials during a sports event is given by C(x) = 20 + 3,000x + 0.01x2. (a) Find the marginal cost function C'(x). HINT [See Example 1.] C'(x) = Use it to estimate how fast the cost is increasing when x = 4. thousand dollars per television commercialCompare this with the exact cost of airing the fifth commercial. The cost is going up at the rate of $ per television commercial. The exact cost of airing the fifth commercial is $ . Thus, there is a difference of $ . (b) Find the average cost function C, and evaluate C(4). HINT [See Example 2.] C(x) = C(4) = thousand dollars per television commercial What does the answer tell you? The average cost of airing the first four commercials is $ per commercial.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.(i) Make a table showing the cost of producing 20,40,60,80 and 100 cupcakes.(ii) Make a table showing the revenue from selling 20,40,60,80 and 100 cupcakes.(iii) Write an algebraic expression representing the cost C as a function of the number of cupcakes x that are produced.(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
- 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. (i) Make a table showing the cost of producing 20,40,60,80 and 100 cupcakes. (ii) Make a table showing the revenue from selling 20,40,60,80 and 100 cupcakes. (iii) Write an algebraic expression representing the cost C as a function of the number of cupcakes x that are produced. (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? I would like for you guys to solve the last 3 parts of the question if possible. Thank you.Use the information in the graph to the right to find the values for the following at an output level of 65 The marginal cost is $55 (Enter a numeric response using an integer.) The total cost is $2925 The variable cost is $2405 The fixed cost is $520 XX Cost 100- 55 45. 37 0 65 Quantity of output MC ATC AVCSuppose a firm’s cost function is C(q) = 4q2 + 16, where C(q) is the total cost, and q is the levelof output.(a) Find variable cost, fixed cost, average cost, average variable cost, and average fixed cost.(b) Show the average cost, marginal cost, and average variable cost curves on a graph.
