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A souvenir store wishes to produce two models of souvenirs: Model A and Model B.
Every model-A souvenir will result to Php14 profit, and
every model-B souvenir will result to Php23 pesos profit.
To manufacture a model-A souvenir, it requires 3 minutes on stage 1 and 4 minutes on stage 2.
A model-B souvenir requires 5 minutes on stage 1, and 4 minutes on stage 2.
There are 270 minutes on stage 1 and 360 minutes on stage 2 for processing order.
How many souvenirs of each model should the store make in order to maximize profit?
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The plots in the post by @Theo are INCORRECT.
Therefore, I came to bring a correct solution.
Let X be the number of model A souvenirs;
Y be the number of model B souvenirs.
objective function:
P(X,Y) = 14X + 23Y
constraint inequalities:
3X + 5Y <= 270 (minutes on stage 1)
4X + 4Y <= 360 (minutes on stage 2)
x >= 0, y >= 0
The feasible domain is shown in the plot below
Plots y = (red) and y = (green)
From the plot, you see that the feasibility domain is a triangle in QI under the red line.
It has the vertices
(X1,Y1) = (0,0) (the origin of the coordinate system);
(X2,Y2) = (0,54) (red line Y-intercept);
(X3,Y3) = (90,0) (red line X-intercept).
The values of the objective function at these points are
R(X1,Y1) = 14*0 + 23*0 = 0;
R(X2,Y2) = 14*0 + 23*54 = 1242;
R(X3,Y3) = 14*90 + 23*0 = 1260.
The objective function is maximal at the point (X3,Y3) = (90,0).
Hence, the optimal solution is X = 90 souvenirs of model A and Y = 0 souvenirs of model B.
If they follow this optimal solution, their maximum profit will be Php 1260.
Solved.
