1)A firm’s cost curve is C = F + 10q - bq2 + q3, where b> 0. a.At what output levels does the MC curve cross the AC and the AVC curves? b.Use calculus to show that the MC curve must cross the AVC at its minimum point.
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1)A firm’s cost curve is C = F + 10q - bq2 + q3, where b> 0.
a.At what output levels does the MC curve cross the AC and the
b.Use calculus to show that the MC curve must cross the AVC at its minimum point.
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- Suppose that the dollar cost of producing x appliances is c(x) = 1000 + 70x-0.1x². a. Find the average cost per appliance of producing the first 100 appliances. b. Find the marginal cost when 100 appliances are produced. c. Show that the marginal cost when 100 appliances are produced is approximately the cost of producing one more appliance after the first 100 have been made, by calculating the latter cost directly. CUCKO The average cost per appliance of producing the first 100 appliances is $ (Round to the nearest cent as needed.) /appliance.Is this graph a valid set of cost curves? True/False1. If the average cost of a plant to produce a "q" unit is explained by the functions below this: C = 0.0003q2 - 0.001q + 4 + 20.000/q a. What is the marginal cost function of product q?b. What is the marginal cost when producing 10 units?c. What is the marginal cost when producing 50 units? 2. If the average cost of a plant to produce a "q" unit is explained by the functions below this: C = 0.0001q2 - 0.002q + 5 + 10.000/q a. What is the marginal cost function of product q?b. What is the marginal cost when producing 20 units?c. What is the marginal cost when producing 100 units?
- 2 The company Shirts Galore has figured its total cost of producing and sclling x units of T-shirts per month is given by the equation C(x) = 120 +2.5x-0.0002r. a) Write a rational function to represent the average cost of producing and selling a shirt. b) If the production level is 1200 shirts per month, find the average cost of producing and selling a shirt. c) If the shirts are sold for $7.98 a shirt, what is the profit realized on producing and selling 1200 shirts per month? d) What price must be charged when selling the shirts for a profit of $7368 to bc made on 1200 shirts in one month? * A large company is considering changingGiven 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 + 0.5Q3Set all variables to their baseline values.9) At what level of output is average cost a minimum?10) What is average cost (AC) at that output?11) What is marginal cost (MC) at that output? BASELINE COSTS TC (BASE) $175,113 AC (BASE) $43.78 MC (BASE) $64.12 NEW COSTS TC (NEW) $175,113 AC (NEW) $43.78 MC (NEW) $64.12 POLICY VARIABLES Output 4,000 Fixed cost 25,000 Tax per unit $0.00 AC(NEW)-MC(NEW) -$20.34
- Assume the cost of making 30 belts $800 the cost of makin 35 belts $900 and the cost equation is linear. The belts are sold for$ 27 each. a)find the marginal cost b)find a linear equation in slope-intercept, form that represent the total Cost of making will c) What is the fixed cost? d) find a profit in slope- intercept that will represent the profit if x belt are made and sold? e) Find the break even point?3. The "Sad Student" Company finds that it costs a total of C(q) = 9720 +500g – 1.5q² +0.005q Dollars to produce q lots of its latest board game named "Calculus Teacher Shooter", each lot consisting of 100 games.. F) Analyze interaction of and derive the formula of this E) Analyze the behavior average cost function marginal cost and average cost numerically relationship with respect to relevant mathematical economics theory and interpret your formulaThe cost curve for producing widgets passes through the following points and is piecewise linear in between. Solve, a. What is the fixed cost of producing 600 widgets? b. What is the variable cost of producing 600 widgets? c. What is the cost per unit if only 400 widgets are produced?
- VI. | Suppose the cost of producing milkshakes is C = Q³/3-30² +150 +50. What is the equation for marginal cost? At what point is marginal cost minimized?Suppose a firm manufactures coffee makers and sells them for $75$75 each. The costs incurred for production and sale of the coffee makers are $1,000$1,000 plus $13$13 for each coffee maker produced.a. Write the function for monthly total costs C(x)=C(x)= b. What is the fixed cost? c. What is the marginal cost? d. Interpret the marginal cost. Each additional coffee maker made decreases the cost by this many dollars. If the number of coffee makers increases by this amount, the cost increases by $1. Each additional coffee maker made yields this many dollars in cost. If the number of units made is increased by this amount, the cost decreases by $1. e. What is C(300)C(300) ? f. Interpret C(300)C(300) When this many coffee makers are produced the cost is $300300. For every additional coffee maker produced the cost increases by this much. This is the cost (in dollars) of producing 300 coffee makers. For each $1 increase in cost this many more coffee makers can…Jenna knits scarves and then sells them on Etsy, an online marketplace. Let C(x) =4x+20 represent the cost C in dollars to produce 1 to 6 scarves. A.) Create a table to show the relationship between the number of scarves x and the cost C. B.) What are the domain and range of C? C.) What is the meaning of C(3)? D.) What is the meaning of the solution to the equation C(x) =40?