Question

A furniture manufacturer wants to maximize profit by producing two types of tables: a coffee table (C) and a dining table (D).

Each coffee table requires 2 square meters of wood and 1 hour of labor.
Each dining table requires 4 square meters of wood and 3 hours of labor.
The manufacturer has a maximum of 100 square meters of wood and 75 hours of labor available per week.
The profit from a coffee table is $50, and from a dining table is $120.
Let C be the number of coffee tables and D be the number of dining tables.

Which objective functions should be maximized, and which set of constraints correctly represents the given information?

Group of answer choices

Objective: Maximize P = 120C + 50D
Constraints: 2C+4D≤100
3C+D≤75
C≥0, D≥0

Objective: Maximize P = 50C + 120D
Constraints: 2C+4D≤100
C+3D≤75
C≥0, D≥0

Objective: Maximize P = 50C + 120D
Constraints: 2C+4D≥100
C+3D≥75
C≥0, D≥0

Objective: Maximize P = 120C + 50D
Constraints: 2C+4D≤100
3C+D≤75
C≥0, D≥0

Answer 1

Correct choice: Objective: Maximize P = 50C + 120D
Constraints: 2C + 4D ≤ 100
C + 3D ≤ 75
C ≥ 0, D ≥ 0

Reason: profit is $50 per coffee and $120 per dining table, wood use is 2C+4D ≤100, labor use is 1C+3D ≤75.