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Polynomials and Rational Functions · Paper 2 — Free Maths AI SL Practice Questions

1MasterySAQ-SPolynomial functions and their graphs8 marksPaper 2~12 min
A small brewery produces craft beer. The profit, in thousands of dollars, from selling xx hundred litres of beer is modelled by P(x)=−0.1x3+1.5x2+3.6x−10,0≤x≤15.P(x) = -0.1x^3 + 1.5x^2 + 3.6x - 10, \quad 0 \leq x \leq 15.
(a)
Write down the value of P(0)P(0) and state what this value represents for the brewery. [2 marks]
(b)
Calculate the number of litres of beer the brewery must sell to break even. Give your answer correct to the nearest litre. [2 marks]
(c)
Determine the maximum profit and the quantity of beer sold at which it occurs. Give the quantity correct to the nearest hundred litres and the profit correct to the nearest thousand dollars. The brewery's storage capacity limits production to 900900 litres. Determine whether operating at maximum profit or at the storage limit gives greater profit, and find the difference in profit in dollars. [4 marks]
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