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Simplifying R(p) = -10p2 + 1000p Multiply R * p pR = -10p2 + 1000p Reorder the terms: pR = 1000p + -10p2 Solving pR = 1000p + -10p2 Solving for variable 'p'. Reorder the terms: -1000p + pR + 10p2 = 1000p + -10p2 + -1000p + 10p2 Reorder the terms: -1000p + pR + 10p2 = 1000p + -1000p + -10p2 + 10p2 Combine like terms: 1000p + -1000p = 0 -1000p + pR + 10p2 = 0 + -10p2 + 10p2 -1000p + pR + 10p2 = -10p2 + 10p2 Combine like terms: -10p2 + 10p2 = 0 -1000p + pR + 10p2 = 0 Factor out the Greatest Common Factor (GCF), 'p'. p(-1000 + R + 10p) = 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 '(-1000 + R + 10p)' equal to zero and attempt to solve: Simplifying -1000 + R + 10p = 0 Solving -1000 + R + 10p = 0 Move all terms containing p to the left, all other terms to the right. Add '1000' to each side of the equation. -1000 + R + 1000 + 10p = 0 + 1000 Reorder the terms: -1000 + 1000 + R + 10p = 0 + 1000 Combine like terms: -1000 + 1000 = 0 0 + R + 10p = 0 + 1000 R + 10p = 0 + 1000 Combine like terms: 0 + 1000 = 1000 R + 10p = 1000 Add '-1R' to each side of the equation. R + -1R + 10p = 1000 + -1R Combine like terms: R + -1R = 0 0 + 10p = 1000 + -1R 10p = 1000 + -1R Divide each side by '10'. p = 100 + -0.1R Simplifying p = 100 + -0.1RSolution
p = {0, 100 + -0.1R}
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