Two types of crops can be grown in particular irrigation area each year. Each unit quantity of crop A can be sold for a price PA and requires WA units of water, LA units of land, FA units of fertilizer, and HA units of labor. Similarly, crop B can be sold at a unit price of PB and requires WB, LB, FB and HB units of water, land, fertilizer, and labor, respectively, per unit of crop. Assume that the available quantities of water, land, fertilizer, and labor are known, and equal W, L, F, and H, respectively. (a) Structure a linear programming model for estimating the quantities of each of the two crops that should be produced in order to maximize total income.
(b) Solve the problem graphically, using the following data:
Resource Crop A Crop B Maximum Available Resources
Water 2 3 60
Land 5 2 80
Fertilizer 3 2 60
Labor 1 2 40
Unit Price 30 25

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?