Section 1.2, 1.3.pptx - SECTION 1.2 Functions Models COST...

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SECTION 1.2 Functions & Models
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COST, REVENUE, & PROFIT A cab’s starting fare is $2.00 on entering the cab, plus $1.80 for each mile. a) Find the cost C of an x-mile trip b) Use the model to find the cost of a 40 mile trip c) What is the cost of the 2 nd mile? 10 th mile? d) Graph it.
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A cab’s starting fare is $2.00 on entering the cab, plus $1.80 for each mile. a) Find the cost C of an x-mile trip b) Use the model to find the cost of a 40 mile trip c) What is the cost of the 2 nd mile? 10 th mile? d) Graph it.
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COST, REVENUE, & PROFIT FUNCTIONS Cost: C(x) = Variable Cost + Fixed Cost C(x) = mx + b (linear cost function) fixed Marginal Cost (cost/unit) Revenue: net sales R(x) = Price per unit × unit ( = mx) Profit = Revenue Cost P(x) = R(x) C(x) BREAK EVEN: P(x) = 0 or R(x) = C(x)
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The cost to manufacture t-shirts is C(x) = 8x +100, and the revenue obtained by manufacturing the t-shirts is R(x) = 10x. What is the daily profit? P(x) = R(x) C(x)
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The annual operating cost of a gym is to be estimated to be C(x) = 100,000 +160x – 0.2x 2 dollars (0 ≤ x ≤ 400), where x is the number of members. The annual revenue is $800 per member. Variable Cost? Fixed Cost? Profit? How many members must the gym have to make a profit?
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DEMAND & SUPPLY MODELS As the Price (p) , Demand (q) The demand for private schools depends on tuition cost, and can be
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