Question

Solve using the graphical method. Choose your variables, identify the objective function and the constraints, graph the constraints, shade the feasibility region, identify all corner points, and determine the solution that optimizes the objective function. Use this information to answer the following 8-part question:

A small company manufactures two types of radios- regular and short-wave. The manufacturing of each radio requires two operations: Assembly and Finishing. The regular radios require 1 hour of Assembly and 3 hours of Finishing. The short-wave radios require 3 hours of Assembly and 1 hour of Finishing. The total labor-hours available per week in the Assembly division is 60, and in the Finishing division, 60. A profit of $50 is realized for every regular radio, and $75 for every short-wave radio. Management wants to determine the number of each type of radio to produce so that profit can be maximized

. (i) Which variable should x define? (Enter letter for correct answer in the blank)

a. number of regular radios produced

b. number of labor-hours needed for assembly

c. total number of radios to produce in order to maximize profit

d. number of labor-hours needed for finishing

(ii) Which variable should y define? (Enter letter for correct answer in the blank)

a. total number of radios to produce in order to maximize profit

b. number of short-wave radios produced

c. number of labor-hours needed for assembly

d. number of labor-hours needed for finishing

(iii) Which of the following correctly defines the constraint on labor-hours for radio assembly? (Enter letter for correct answer in the blank)

a. 3x+y≤60

b. x+3y≤60

c. x+3y≥60

d. 3x+y≥60

(iv) Which of the following correctly defines the constraint on labor-hours needed for radio finishing? (Enter letter for correct answer in the blank)

a. 3x+y≥60

b. x+3y≥60

c. x+3y≤60

d. 3x+y≤60

(v) Which of the following correctly defines the objective function? (Enter letter for correct answer in the blank)

a. P=60x+60y

b. P=75x+50y

c. P=50x+75y

d. P=300x+4500y

(vi) Which of the following sets of corner points correctly defines the feasible region for this system of linear inequalities? (Enter letter for correct answer in the blank)

a. (0,20) ; (0,60) ; (15,15)

b. (0,20) ; (0,0) ; (20,0) ; (15,15)

c. (0,60) ; (15,15) ; (60,0)

d. (15,15) ; (20,0) ; (60,0)

(vii) Based on your determination of the feasible region for this business process, how many radios of each type should be produced in order to maximize profit? (Enter letter for correct answer in the blank)

a. 0 regular radios and 20 shortwave radios

b. 20 regular radios and 0 shortwave radios

c. 15 regular radios and 15 shortwave radios

d. 0 regular radios and 60 shortwave radios

(viii) Which of the following is the correct value for the maximum total profit made from producing the optimum number of each type of radio?

a. P=$4500

b. P=$3000

c. P=$1500

d. P=$1875

Answer 1

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