Neveah’s bag contains 2 red marbles, 3 blue marbles and 5 green marbles. Neveah randomly selects a marble from the bag, records the color and then puts the marble back the bag. If she does the 150 times how many times would she expect to select blue

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dani4685

02.01.2020

Mathematics

The profit is given by the subtraction of revenue and cost. So, the function for the profit is

$P(x) = R(x) - C(x) = 60x-0.1x^2 - (6x+15) = 60x-\frac{1}{10}x^2 - 6x-15 = -\frac{1}{10}x^2 + 54x - 15$

We want to maximize this function, so let's derive its expression and set it to zero:

$P'(x) = -\frac{1}{5}x + 54 = 0 \iff -\frac{1}{5}x = -54 \iff x = 270$

For this number of units, the profit equals

$P(270) = -\frac{1}{10}(270)^2 + 54\cdot 270 - 15 = 7275$

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