A Manufacturer Produces Two Models of Desks

question 4

Essay

A manufacturer produces two models of desks. Model A requires 5 hr to stain and finish and 4 hr to assemble. Model B requires 4 hr to stain and finish and 1 hr to assemble. The total amount of time available for staining and finishing is 40 hr and for assembling is 16 hr. Let x represent the number of Model A desks produced, and let y represent the number of Model B desks produced.
a. Write two inequalities that express the fact that the number of desks to be produced cannot be negative.
b. Write an inequality in terms of the number of Model A and Model B desks that can be produced if the total time for staining and finishing is at most 24 hr.
c. Write an inequality in terms of the number of Model A and Model B desks that can be produced if the total time for assembly is no more than 16 hr.
d. Graph the feasible region formed by graphing the preceding inequalities.
e. Is the point (1, 5) in the feasible region? What does the point (3, 1) represent in the context of this problem?
f. Is the point (4, 8) in the feasible region? What does the point (5, 4) represent in the context of this problem?

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Definitions:

Fixed Calipers

Brake calipers that are mounted in a stationary position with pistons arranged on opposing sides of the rotor, applying brake pressure evenly.

Drum Brake Micrometer

A tool used to measure brake drum diameter and to check for out-of-round.

Out-of-round

A condition where a component, such as a rotor or drum, is not perfectly circular, leading to uneven wear or vibration.

Nonfloating Drum

A type of drum in machinery or equipment that is fixed in place and does not move or float axially under operation.