SOLUTION: the manager of a nearby cafe found that the cost to produce 100 cups of coffee is $11.02, while the cost to produce 400 cups is $40.12 . Each cup of coffee is sold for 75 cents per

Algebra ->  Probability-and-statistics -> SOLUTION: the manager of a nearby cafe found that the cost to produce 100 cups of coffee is $11.02, while the cost to produce 400 cups is $40.12 . Each cup of coffee is sold for 75 cents per      Log On


   

Question 466896: the manager of a nearby cafe found that the cost to produce 100 cups of coffee is $11.02, while the cost to produce 400 cups is $40.12 . Each cup of coffee is sold for 75 cents per cup. Asume the cost c(x) is a linear function od x, the number of cups produced.
How many cups of coffee will the cafe have to sell in order to break even? c(x)= r(x).

How many cups of coffee will need to sold in order to make a profit of 4500? round to the nearst cup?
Answer by Big Poop(157) About Me  (Show Source):
You can put this solution on YOUR website!
sdgfERROR Algebra::Solver::Engine::invoke_solver_noengine: solver not defined for name 'linear_egfsdqguation'.
Error occurred executing solver 'linear_egfsdqguation' .
Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc
this equation defines a vertical line.

  • X intercept: 2. X intercept is the intersection of the line with the x axis.

  • Y intercept: not defined (the line IS vertical)

  • Slope: not defined, can be thought of as infinite

graph%28+500%2C+500%2C+2-5%2C+2%2B5%2C+-10%2C+10%2C+1000000x-1000000%2A2+%29+
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-2x%2B-3+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-2%29%5E2-4%2A1%2A-3=16.

Discriminant d=16 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--2%2B-sqrt%28+16+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-2%29%2Bsqrt%28+16+%29%29%2F2%5C1+=+3
x%5B2%5D+=+%28-%28-2%29-sqrt%28+16+%29%29%2F2%5C1+=+-1

Quadratic expression 1x%5E2%2B-2x%2B-3 can be factored:
1x%5E2%2B-2x%2B-3+=+1%28x-3%29%2A%28x--1%29
Again, the answer is: 3, -1. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-2%2Ax%2B-3+%29
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