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Simplifying R(p) = -4p2 + 200p Multiply R * p pR = -4p2 + 200p Reorder the terms: pR = 200p + -4p2 Solving pR = 200p + -4p2 Solving for variable 'p'. Reorder the terms: -200p + pR + 4p2 = 200p + -4p2 + -200p + 4p2 Reorder the terms: -200p + pR + 4p2 = 200p + -200p + -4p2 + 4p2 Combine like terms: 200p + -200p = 0 -200p + pR + 4p2 = 0 + -4p2 + 4p2 -200p + pR + 4p2 = -4p2 + 4p2 Combine like terms: -4p2 + 4p2 = 0 -200p + pR + 4p2 = 0 Factor out the Greatest Common Factor (GCF), 'p'. p(-200 + 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 '(-200 + R + 4p)' equal to zero and attempt to solve: Simplifying -200 + R + 4p = 0 Solving -200 + R + 4p = 0 Move all terms containing p to the left, all other terms to the right. Add '200' to each side of the equation. -200 + R + 200 + 4p = 0 + 200 Reorder the terms: -200 + 200 + R + 4p = 0 + 200 Combine like terms: -200 + 200 = 0 0 + R + 4p = 0 + 200 R + 4p = 0 + 200 Combine like terms: 0 + 200 = 200 R + 4p = 200 Add '-1R' to each side of the equation. R + -1R + 4p = 200 + -1R Combine like terms: R + -1R = 0 0 + 4p = 200 + -1R 4p = 200 + -1R Divide each side by '4'. p = 50 + -0.25R Simplifying p = 50 + -0.25RSolution
p = {0, 50 + -0.25R}
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