Profit function, Objective Function, Constraints?

Question

A store owner stocks two types of dishwashers and has warehouse space for at most 36 units. The owner keeps at least twice as many of model A as model B. If the profit on model A is $24 and the profit on model B is $36, how many of each should the owner stock to maximize the profit? What is the objective function and constraints?PR

Answer 1

Say no of model A units=y

No of model B units =x

 

Objective function----

Max z= (36x +24y)

 

Constraints------

x+y<=36

y>=2x

 

Solving the above, we have the corner points as

(0,0) , (0,36) , (12,24)

 

Checking value of objective function at these corner points

z=0. At (0,0)

z=864 at (0,36)

z=1008 at (12,24)

 

So maximum is at (12,24)

x=12

y=24