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Simplifying s(p) = -50p2 + 3000p Multiply s * p ps = -50p2 + 3000p Reorder the terms: ps = 3000p + -50p2 Solving ps = 3000p + -50p2 Solving for variable 'p'. Reorder the terms: -3000p + ps + 50p2 = 3000p + -50p2 + -3000p + 50p2 Reorder the terms: -3000p + ps + 50p2 = 3000p + -3000p + -50p2 + 50p2 Combine like terms: 3000p + -3000p = 0 -3000p + ps + 50p2 = 0 + -50p2 + 50p2 -3000p + ps + 50p2 = -50p2 + 50p2 Combine like terms: -50p2 + 50p2 = 0 -3000p + ps + 50p2 = 0 Factor out the Greatest Common Factor (GCF), 'p'. p(-3000 + s + 50p) = 0Subproblem 1
Set the factor 'p' equal to zero and attempt to solve: Simplifying p = 0 Solving p = 0 Move all terms containing p to the left, all other terms to the right. Simplifying p = 0Subproblem 2
Set the factor '(-3000 + s + 50p)' equal to zero and attempt to solve: Simplifying -3000 + s + 50p = 0 Reorder the terms: -3000 + 50p + s = 0 Solving -3000 + 50p + s = 0 Move all terms containing p to the left, all other terms to the right. Add '3000' to each side of the equation. -3000 + 50p + 3000 + s = 0 + 3000 Reorder the terms: -3000 + 3000 + 50p + s = 0 + 3000 Combine like terms: -3000 + 3000 = 0 0 + 50p + s = 0 + 3000 50p + s = 0 + 3000 Combine like terms: 0 + 3000 = 3000 50p + s = 3000 Add '-1s' to each side of the equation. 50p + s + -1s = 3000 + -1s Combine like terms: s + -1s = 0 50p + 0 = 3000 + -1s 50p = 3000 + -1s Divide each side by '50'. p = 60 + -0.02s Simplifying p = 60 + -0.02sSolution
p = {0, 60 + -0.02s}
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