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A company produces two types of shoes – casual, and athletic – at its two factories,

/in /by

A company produces two types of shoes – casual,
and athletic – at its two factories, Factory I and Factory II. Daily production at each factory for number of pairs of each type of shoe is listed below:

Factory I Factory II
Casual 100 200
Athletic 300 100

The company must produce at least 8000 pairs of casual shoes, and 9000 pairs of athletic shoes. The cost of operating Factory I is $1500 per day and the cost of operating Factory II is $2000. Management needs to determine the number of days each factory needs to operate to meet production goals at minimum cost.

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

a. number of pairs of athletic shoes produced
b. number of days Factory I operates
c. number of pairs of casual shoes produced
d. cost to produce a pair of athletic shoes

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

a. number of pairs of athletic shoes produced
b. cost to produce a pair of casual shoes
c. number of pairs of casual shoes produced
d. number of days Factory II operates

(iii) Which of the following correctly defines the constraint on total daily production of pairs of casual shoes?

a. 200x+100y≤8000
b.100x+200y≤8000
c.200x+100y≥8000
d.100x+200y≥8000

(iv) Which of the following correctly defines the constraint on total daily production of pairs of athletic shoes?

a.300x+100y≥9000
b.100x+300y≥9000
c.300x+100y≤9000
d.100x+300y≤9000

(v) Which of the following correctly defines the objective function?

a. C=8000x+9000y
b.C=9000x+8000y
c.C=1500x+2000y
d.C=2000x+1500y

(vi) Which of the following sets of corner points correctly defines the feasible region for this system of linear inequalities?

a. (0, 0) ; (40, 0) ; (20, 30) ; (30, 0)
b. (0, 40) ; (0, 90) ; (20, 30)
c. (0, 90) ; (20, 30) ; (80, 0)
d. (20, 30) ; (30, 0) ; (80, 0)

(vii) Based on your determination of the feasible region for this business process, how many days should each factory operate to meet production goals at minimum cost?

a. 30 days for Factory I and 0 days for Factory II
b. 20 days for Factory I and 30 days for Factory II
c. 0 days for Factory I and 40 days for Factory II
d. None of these answers are correct

(viii) Which of the following is the correct value for the minimum cost to meet production goals for both types of shoes?
a. C = $45000
b. C = $80000
c. C = $90000
d. C = $120000

 
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