Question

A furniture manufacturing company manufactures dining-room tables and chairs. A table requires 8 labor-hour s for assembling and 2 labor-h ours for finishing. A chair requires 2 labor-hours for assembling and 1 labor-hour for finishing. The maximum labor-hours available p er day for assembly and finishing are 400 and 120, respectively. If x is the number of tables and y is the number of chairs produced per day, write a system of linear inequalities that indicates appropriate restraints on x and y.

Required:
Find the set of feasible solutions graphically for the number of tables and chairs that can be produced.

Answer 1

See Annex In blue feasible region ( using Geogebra)

Explanation:

Table 1.-

Assembling hours finishing hours

Product (tables) x 8 2

Product ( chairs) y 2 1

Availability 400 120

Constrains:

1.-Availability of assembling hours 400

8*x + 2* y ≤ 400

2.-Availability of Finishing hours

2*x + 1*y ≤ 120

3.-General constraints

x ≥ 0 y ≥ 0 integers