1. Bedrock Stone and Gravel Company sells bags of gravel to their customers. If

Question

1. Bedrock Stone and Gravel Company sells bags of gravel to their customers. If the cost of producing x bags of gravel is given by the function C(x) 0.09x2-67x+784 and the revenue generated from the sale of x bags of gravel is given by the function R(x)-0.01x2-17x (a Show all work to find the profit function P(x) (b) Use your P(x) function from 1(a) and the quadratic formula to find the number of bags of gravel that must be sold for a S2000 profit. Show all work. 2. Use the quadratic formula to solve 25x2 +9-4x for the variable x

Explanation / Answer

1) C(x) = 0.09x^2 - 67x + 784

R(x) = - 0.01x^2 - 17x

P(x) = R(x) - C(x)

= - 0.01x^2 - 17x - (0.09x^2 - 67x + 784 )

P(x) = -0.01x^2 + 50x - 784

b) plugging P(x) = 2000

2000 =  -0.01x^2 + 50x - 784

-0.01x^2 + 50x - 2784 = 0

x = [ - 50 +- sqrt ( 50^2 - 4*2784*.01) ] / 2*-0.01

x = 56.3 , 4943.7

so, either 56 or 4944 bags must be sold for a $ 2000 profit

2) 25x^2 + 9 = 4x

subtracting 4x from both sides

25x^2 - 4x + 9 = 0

applying quadratic formula

x = [ 4 +- sqrt ( 16 - 4*9*25 ) ] / 50

x = ( 2 +- i sqrt 221 ) / 25

x = ( 2 + i sqrt 221 ) / 25 , ( 2 - i sqrt 221 ) / 25

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