Question

The Wellbuilt Company produces two types of wood chippers, economy and deluxe. The deluxe model requires 3 hours to assemble and 1/2 hour to paint, and the economy model requires 2 hours to assemble and 1 hour to paint. The maximum number of assembly hours available is 24 per day, and the maximum number of painting hours available is 6 per day.
(a) Write the system of inequalities that describes the constraints on the number of each type of wood chipper produced. (Let x represent the number of deluxe models, and let y represent the number of economy models.)
(b) Find the corners of the solution region. (Order your answers from smallest to largest x, then from smallest to largest y.)

Answer 1

Answer:  

For assemble     3*x  + 2*y  ≤ 24    (1)

For painting       0,5*x + 1*y ≤ 6      (2)

The feasible region is fomed by to triangles ( see annex)

Step-by-step explanation:

We have :

-    x    number of the luxe model

so for each x    we need  3 hours for assemble and  1/2 hour for painting

-    y    numbe of economy model

so for each y   we need 2 hours for assemble and 1 hour for painting

Total hours available for assemble 24 per day

Total hours available for painting  6 per day

a)

For assemble     3*x  + 2*y  ≤ 24    (1)

For painting       0,5*x + 1*y ≤ 6      (2)

b)  In inequality (1)

if we poduce 0 de luxe model,  we can assemble up to 12 economy model

and if we produce 0 economy model  we can assamble up to 8 de luxe model. Therefore the feasible region for that constraint is

x  (the luxe model )    from 0 up to maximum of 8 units

y (economy model )   from 0 up to maximum of 12 units

We have to examine the (2) constraint

x      from 0  up to 12 units

y      from 0 up tp  6 units