Consider the following. optimize f(r, p) = 412 + rp - p2 + p [subject to g(r, p) = 4r + 3p = 1 (a) Write the Lagrange system of partial derivative equations. (Enter your answer as a comma-separated list of equations. Use ) to represent the Lagrange multiplier.) (b) Locate the optimal point of the constrained system. (Enter an exact number as an integer, fraction, or decimal.) Once you have the answer matrix on the homescreen of your calculator, hit MATH ENTER ENTER to convert any decimal approximations to exact values. Do the same after you've evaluated fat r and p to convert the approximated output value to an exact value. (r, p, f(r, P) ) =