SOLUTION: A manufacturer produces three models of bicycles. The time (in hours) required for assembling, painting, and packaging each model is as follows. Model A Model B Model C Assembl

A manufacturer produces three models of bicycles. The time
(in hours) required for assembling, painting, and packaging
each model is as follows.
           Model A  Model B  Model C
Assembling   2       2.5       3
Painting     1.5     2         1
Packaging    1       0.75      1.25
The total time available for assembling, painting, and packaging is 4006 hours, 2495 hours and 1500 hours, respectively.
The profit per unit for each model is $45 (Model A), $50 (Model B), and $55 (Model C). 
How many of each type should be produced to obtain a maximum profit?

x bicycles of model A;

y bicycles of model B;

z bicycles of model C.


The profit function

P(x,y,z) = 45x + 50y + 55z            (1)    (= objective function, dollars)



Restrictions:

2x   +   2.5y   +  3z    <= 4006      (2)   (assembling, hours)

1.5x +   2y     +  1z    <= 2495      (3)   (painting, hours)

1x   +   0.75y  +  1.25z <= 1500      (4)   (packaging, hours)

x >= 0,  y >= 0,  z >=  0             (5)   (standard non-negativity restrictions)



Now go to the site https://www.zweigmedia.com/RealWorld/simplex.html

and use free of charge solver there.


Input the profit function and the restrictions and press the "Solve" button.


It will solve this maximization problem using the Linear Programming method / (the "simplex method").


The solver produces this solution (this answer)


   X = 322 bicycles of type A;  Y = 764 bicycles of type B;  Z = 484 bicycles of type C;  p = $79310.    ANSWER

Maximize p = 45x + 50y + 55z subject to
2x   +   2.5y   +  3z    <= 4006 
1.5x +   2y     +  1z    <= 2495
1x   +   0.75y  +  1.25z <= 1500
x >= 0  
y >= 0
z >= 0