Solve dU/dt = d^2U/dx^2,0 < x < 6, t > 0, subject to the conditions U(0,t) = U(6,t)=0, U(x,0)=( 1 if 0<= x <= 3 & 0 if 3 <= x <= 6). Interpret physically.

Acoffee shop orders at most $3,500 worth of coffee and tea. the shop needs to make a profit of at least $1,900 on the order. the possible combinations of coffee and tea for this order are given by this system of inequalities, where c = pounds of coffee and t = pounds of tea: 6c + 13t ≤ 3,500 3.50c + 4t ≥ 1,900 which graph's shaded region represents the possible combinations of coffee and tea for this order?