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20.) The price of a certain product varies according to how much is available. At a production level of x units the price per units the price per unit is 3.40-0.01x.
a.) What is the revenue if x units are produced and sold?

Revenue function R(x) = x(3.40 - 0.01x)

b.) If the cost of producing x units is 100+1.20x, find the profit function and the break-even points.

Profit function P(x) = revenue - cost
= x(3.40 - 0.01x) - (100+1.20x)
= 3.40x - 0.01x^2 - 100 - 1.20x
= -0.01x^2 + 2.2x - 100

Break even occurs when profit = 0

-0.01x^2 + 2.2x - 100 = 0
Multiply by -100
x^2 - 220x + 10000 = 0
which will give

x = 64.1742, 155.826

If we round up x = 65, 156

Thus, break even points occur at x = 65, 156

21.) A theater company charges the same price for all tickets, regardless of day of the week or seat location. It has found that a price of $16 it sells 900 tickets a week, but at a price of $20 per ticket it only sells 780. Assume that q, the ...

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