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Let X and Y be the numbers of model A sets and model B sets, respectively.
Then the constrains are
30 <= X <= 60,
10 <= Y <= 30,
X + Y <= 60.
The profit function is C(X,Y) = 40*X + 60*Y dollars to maximize.
The feasibility area is shown in the Figure below
Plots X = 30 (red), X = 60 (green), Y = 10 (blue), Y = 30 (magenta) and X + Y = 60.
The feasibility domain is the triangle area bounded by the red, blue and sloped lines.
The points to check the cost function are
P1 = (30,10) (right angle vetex)
P2 = (30,30) (upper vertex of the triangle)
P3 = (50,10) (most right vertex of the triangle).
The values of the profit function are
at P1: P(30,10) = 30*40 + 10*60 = 1800;
at P2: P(30,30) = 30*40 + 30*60 = 3000;
at P3: P(50,10) = 50*40 + 10*60 = 2600.
You are looking for the maximum - hence, your solution is at P2.
Answer. 30 model A sets and 30 model B sets is the solution which provides the maximal profit of $3000 per day.
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To see other similar problems solved by the same method, look into the lesson
- Solving minimax problems by the Linear Programming method
in this site.