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  3. consider the following. optimize f(r, p) = 3r2

Consider the following. optimize f(r, p) = 3r2 + rp − p2 + p subject to g(r, p) = 3r + 4p...

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Question

Basic Math

Consider the following.

optimize f(r,p) = 3r2 +rp − p2 +p
subjectto g(r, p) =3r + 4p = 1

(a) Write the Lagrange system of partial derivative equations.(Enter your answer as a comma-separated list of equations. Useλ to represent the Lagrange multiplier.)

(b) Locate the optimal point of the constrained system. (Enteran exact number as an integer, fraction, or decimal.)

Once you have the answer matrix on the homescreen of yourcalculator, hit MATH ENTER ENTER to convert any decimalapproximations to exact values. Do the same after you've evaluatedf at r and p to convert the approximated output value to an exactvalue.

(r,p,f(r,p)) =

(c) Identify the optimal point as either a maximum point ora minimum point

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