Use Lagrange multiplier techniques to find the local extreme values of the given function subject to the stated constraint. If appropriate, determine if the extrema are global. (If a local or global extreme value does not exist enter DNE.) f(x, y)

A3-mm-thick panel of aluminum alloy (k 177 w/m-k, c 875 j/kg-k and ? = 2770 kg/m) is finished on both sides with an epoxy coating that must be cured at or above t,-150°c for at least 5 min. the production line for the curing operation involves two steps: (1) heating in a large oven with air at ts,0-175°c and a convection coefficient of h, 40 w/m2. k, and (2) cooling in a large chamber with air at 25°c and a con- vection coefficient of he 10 w/m2.k. the heating portion of the process is conducted over a time interval te which exceeds the ime required to reach 150°c by 5 min (h = r + 300 s). the coating has an emissivity of ? = 0.8, and the temperatures of the oven and chamber walls are 175 and 25°c, respectively. if the panel is placed in the oven at an initial temperature of 25°c and removed from the chamber at a safe-to-touch tempera ture of 37°c, what is the total elapsed time for the two-step curing operation?

Agas contained within a piston-cylinder assembly e end nation about same energy states, 1 and 2, where pi 10 bar, v undergoes two processes, a and b, between the sam 0.1 m3, ui-400 kj and p2 1 bar, v2 1.0 m2, u2 200 kj: process a: process from 1 to 2 during which the pressure- volume relation is pv constant process b: constant-volume process from state 1 to a pressure of 2 bar, followed by a linear pressure-volume process to +20 0 state 2 kinetic and potential energy effects can be ignored. for each of the processes a and b, (a) sketch the process on p-v coordinates, (b) evaluate the work, in kj, and (c) evaluate process the heat transfer, in kj

Determine the time of the day and month of the year at which the peak sensible cooling load occurs for a top floor, north-eastern corner room of an office building in durban for the following conditions: floor area: 8 x 8 x 3 m east and north walls: 115 mm face brick (outside), 20 mm air space, 115 mm ordinary brick (inside) with 15 mm plaster roof construction: suspended plasterboard ceiling, 450 mm air space, 150 mm concrete, 75mm screed, waterproofing no heat transfer across other surfaces window area 3x 1,5 m high in north wall only. ordinary glass with venetian blinds. lights and occupants : from 07: 00 to 18: 00 average light density: 25 w/m2 number of occupants : 5 seated, light office work room temperature 24°c