(a) Use the total differential to estimate (3+70.01)2+8(270.01)2(4+70.01)2. Leave your numerical answer in 3 decimal places. (b) Find and classify the critical points of f(x,y)=14xy2+3(7+3)x2y(7+2)(7+3)xy. (c) The goal of consumers is to maximize utility from a given budget. Assume there are three commodities with amounts x,y, and z, and prices are $5,$7 and $14 respectively. The budget of the consumer is $1470 and the utility function is given to be U=xyz. Use the method of Lagrange Multipliers, find the maximum utility value U which can fully utilize the budget. (a) Use the total differential to estimate (3+70.01)2+8(270.01)2(4+70.01)2. Leave your numerical answer in 3 decimal places. (b) Find and classify the critical points of f(x,y)=14xy2+3(7+3)x2y(7+2)(7+3)xy. (c) The goal of consumers is to maximize utility from a given budget. Assume there are three commodities with amounts x,y, and z, and prices are $5,$7 and $14 respectively. The budget of the consumer is $1470 and the utility function is given to be U=xyz. Use the method of Lagrange Multipliers, find the maximum utility value U which can fully utilize the budget