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.)

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jtellezd jtellezd · Answer 1 · 2019-11-11T17:25:40+01:00

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