Rates of Change: Velocity and Marginals

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Presentation transcript:

Rates of Change: Velocity and Marginals

1. Find the marginal cost for producing x units 1. Find the marginal cost for producing x units. (The cost is measured in dollars). (similar to p.114 #22)

2. Find the marginal revenue for producing x units 2. Find the marginal revenue for producing x units. (The revenue is measured in dollars). (similar to p.114 #26)

3. Find the marginal profit for producing x units 3. Find the marginal profit for producing x units. (The profit is measured in dollars). (similar to p.115 #30)

4. The revenue R (in dollars) from renting x apartments can be modeled by R = 3x(800 + 40x - x2) (a) Find the additional revenue when the number of rentals is increased from 10 to 11 (algebra method). (b) Find the marginal revenue when x = 10 (calculus method) (c) Compare the results of parts (a) and (b) (similar to p.115 #32)

5. Profit. The monthly demand function and cost function for x newspapers are given by p = 4 - 0.002x and C = 40 + 2.3x (a) Find the monthly revenue R as a function of x (R = xp) (b) Find the monthly profit P as a function of x (P = R - C) (c) Complete the table below (similar to p.115 #38) X 300 600 900 1200 1500 dR/dx dP/dx P

6. Marginal Profit. When the admission price was $5 per ticket, 40000 tickets were sold. When the price was raised to $6, only 30000 tickets were sold. Assume that the demand function is linear and that the variable and fixed costs are $0.15 and $90000, respectively. (a) Find the profit P as a function of x, the number of tickets sold (b) Find the marginal profits when 10000 tickets are sold and when 30000 tickets are sold (similar to p.116 #40)