Question

please help thank you

Consider the following optimize f,p)42+ 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 λ to represent the Lagrange multiplier.) (b) Locate the optimal point of the constrained system. (Enter an exact number as an integer, fractin, or decimal.) Once you have the answer matrix on the homescreen of your calculator, hit MATH ENTER ENTER to convert any decimaí 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)) (c) Identify the optimal point as either a maximum point or a minimum point. minimum

Answer 1

dutom iven that (a) Hese, Wsite the Lange ystem oP Paatial denivartive equations That is

(b) nloeo Locate the optimas point of comstsained point o ystem attons e qet IIA-1 and I Ft by Substitutina these. values n eq) We get 1

l6 tHence lb and P8- 20x3 tb は tence l6 4 an d 64 16, за 3& 32

(c) Hese he optimal pont e elobal minimum Thanking yau--