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Simplifying R(p) = -4p2 + 4000p Multiply R * p pR = -4p2 + 4000p Reorder the terms: pR = 4000p + -4p2 Solving pR = 4000p + -4p2 Solving for variable 'p'. Reorder the terms: -4000p + pR + 4p2 = 4000p + -4p2 + -4000p + 4p2 Reorder the terms: -4000p + pR + 4p2 = 4000p + -4000p + -4p2 + 4p2 Combine like terms: 4000p + -4000p = 0 -4000p + pR + 4p2 = 0 + -4p2 + 4p2 -4000p + pR + 4p2 = -4p2 + 4p2 Combine like terms: -4p2 + 4p2 = 0 -4000p + pR + 4p2 = 0 Factor out the Greatest Common Factor (GCF), 'p'. p(-4000 + R + 4p) = 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 '(-4000 + R + 4p)' equal to zero and attempt to solve: Simplifying -4000 + R + 4p = 0 Solving -4000 + R + 4p = 0 Move all terms containing p to the left, all other terms to the right. Add '4000' to each side of the equation. -4000 + R + 4000 + 4p = 0 + 4000 Reorder the terms: -4000 + 4000 + R + 4p = 0 + 4000 Combine like terms: -4000 + 4000 = 0 0 + R + 4p = 0 + 4000 R + 4p = 0 + 4000 Combine like terms: 0 + 4000 = 4000 R + 4p = 4000 Add '-1R' to each side of the equation. R + -1R + 4p = 4000 + -1R Combine like terms: R + -1R = 0 0 + 4p = 4000 + -1R 4p = 4000 + -1R Divide each side by '4'. p = 1000 + -0.25R Simplifying p = 1000 + -0.25RSolution
p = {0, 1000 + -0.25R}
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