Cost, revenue, and profit are in dollars and x is the number of units. Suppose that the total revenue function for a product is R(x) = 45x and that the total cost function is C(x) = 2000 + 25x + 0.01x². (a) Find the profit from the production and sale of 500 units. (b) Find the marginal profit function. Cost, revenue, and profit are in dollars and x is the number of units. Suppose that the total revenue function is given by R(x) = 48x and that the total cost function is given by C(x)=90 +29x + 0.1x². (a) Find P(100). P(100) = (b) Find the marginal profit function MP. MP = (c) Find MP at x = 500. MP = Explain what it predicts. The total profit will ---Select--- by approximately $ on the sale of the next (501st) unit. (c) Find MP at x = 100. MP(100) = (d) Find P(501) - P(500). $ Explain what this value represents. This is the total cost of 501 units. This is the total profit for 501 units. This is the actual profit on the sale of the 501st unit. This is the actual revenue on the sale of the 501st unit. This is the actual cost of the 501st unit. Explain what it predicts. O At x = 100, MP(100) predicts that cost will decrease by IMP(100) | dollars. ○ At x = 100, MP(100) predicts that profit will decrease by IMP(100) | dollars. ○ At x = 100, MP(100) predicts that profit will increase by | MP(100) | dollars. ○ At x = 100, MP(100) predicts that cost will increase by IMP(100) | dollars. (d) Find P(101) - P(100). $ Explain what this value represents. O The sale of the 101st unit will decrease profit by IP(101) P(100) dollars. The sale of the 100th unit will decrease profit by IP(101) - P(100)| dollars. ○ The sale of the 101st unit will increase profit by IP(101) - P(100) | dollars. O The sale of the 100th unit will increase profit by |P(101) - P(100) | dollars. Cost is in dollars and x is the number of units. Find the marginal cost functions MC for the given cost function. C = 900 + 22x + 2x3 MC = Cost, revenue, and profit are in dollars and x is the number of units. If the total profit function is P(x) = 7x - 24, find the marginal profit MP. MP = Suppose that the cost function for a commodity is C(x)=80+x2 dollars. (a) Find the marginal cost at x = 6 units. MC(6)= Tell what this predicts about the cost of producing 1 additional unit. The cost to produce the 7th unit is predicted to be $ (b) Calculate C(7) - C(6) to find the actual cost of producing 1 additional unit. If the cost function for a commodity is C(x) = 1x36x2+6x+ 18 dollars 90 find the marginal cost MC at x = 9 units. (Round your answer to two decimal places.) MC = $ Tell what the marginal cost predicts about the cost of producing 1 additional unit. The cost of producing 1 additional unit is $ Tell what the marginal cost predicts about the cost of producing 2 additional units. The cost of producing 2 additional units is $ What does this mean? This is the total revenue. This is the total profit. The next unit sold earns this much profit. The next unit sold costs this much to make. O This is the total cost.