Question 1127117
<br>
The constraint inequalities are...<br>
{{{x+y <= 5}}}  1 unit of milk for each of A and B; 5 units available<br>
{{{3x+2y <= 12}}}  3 units of chocolate for A, 2 units for B; 12 units available<br>
Graph the constraint equations and find the point of intersection to determine the feasibility region.<br>
{{{graph(400,400,-2,6,-2,6,5-x,6-1.5x)}}}<br>
The intersection point (algebraically, or from the graph) is (2,3).<br>
The objective function for the problem is the total profit, which is $6 per unit for A and $5 per unit for B:  {{{6x+5y}}}.  Evaluate the objective function at each corner of the feasibility region: (0,0), (0,5), (2,3), and (4,0).<br>
(0,0): 6x+5y = 0
(0,5): 6x+5y = 25
(2,3): 6x+5y = 12+15 = 27
(4,0): 6x+5y = 24<br>
The maximum profit is when they make 2 units of A and 3 units of B.