Question 1127117: a chocolate manufacturing company produces only two types of chocolate, A and B. On each sale, the company makes a profit of $6 per unit of A sold and $5 per unit of B sold. Both the chocolates require milk and chocolate only. Each unit of A requires 1 unit of milk and 3 units of chocolate. Each unit of B requires 1 unit of milk and 2 units of chocolate. The company kitchen has a total of 5 units of milk and 12 units of chocolate. The company wishes to maximize its profit. How many units of A and B should it produce respectively? Let the total number of units produced of A equal x and the total number of units of B produced by y. Note: Number of units can only be positive.
Answer by greenestamps(13200)   (Show Source):
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The constraint inequalities are...
 1 unit of milk for each of A and B; 5 units available
 3 units of chocolate for A, 2 units for B; 12 units available
Graph the constraint equations and find the point of intersection to determine the feasibility region.
The intersection point (algebraically, or from the graph) is (2,3).
The objective function for the problem is the total profit, which is $6 per unit for A and $5 per unit for B:  . Evaluate the objective function at each corner of the feasibility region: (0,0), (0,5), (2,3), and (4,0).
(0,0): 6x+5y = 0
(0,5): 6x+5y = 25
(2,3): 6x+5y = 12+15 = 27
(4,0): 6x+5y = 24
The maximum profit is when they make 2 units of A and 3 units of B.
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