A rectangular corral with a total area of 60 square meters is to be fenced off and then divided into 2 rectangular sections by a fence down the middle. The fencing for the outside costs $9 per running meter, whereas that for the interior dividing fence costs $12 per running meter. Which of the following statements hold, if the cost (c) of the fencing is to be maximized? (I) The constraint equation is 3w + 2 l = 60 .
(II) The objective equation is 2l ∙ w = 60 .
(III) The constraint equation is w ∙ l = 60 .
(IV) The objective equation is C = 30w + 18l .
(V) The constraint equation is C = 12w + 9wl .
(VI) The objective equation is C = 60 - lw .
A) III and IV
B) V and VI
C) I and II
D) none of these

Question

A rectangular corral with a total area of 60 square meters is to be fenced off and then divided into 2 rectangular sections by a fence down the middle.  The fencing for the outside costs $9 per running meter, whereas that for the interior dividing fence costs $12 per running meter. Which of the following statements hold, if the cost (c) of the fencing is to be maximized? (I) The constraint equation is 3w + 2 l = 60 .
(II) The objective equation is 2l ∙ w = 60 .
(III) The constraint equation is w ∙ l = 60 .
(IV) The objective equation is C = 30w + 18l .
(V) The constraint equation is C = 12w + 9wl .
(VI) The objective equation is C = 60 - lw .
A) III and IV 
B) V and VI 
C) I and II 
D) none of these

Quizplus · Accepted Answer

The total area of the corral is given as 60 square meters. Let the length of the corral be l and the width be w.

Constraint equation: 
The constraint equation relates to the total area of the corral, which is given as 60 square meters. Therefore, the correct constraint equation is 
w ∙ l = 60

Objective equation: 
The objective equation relates to the cost of the fencing. The cost of the outer fencing is $9 per running meter, and that of the interior dividing fence is $12 per running meter. Therefore, the correct objective equation is 
C = 2(9w + 12l) = 18w + 24l = 30w + 2(9l) = 30w + 18l

Therefore, the correct choices are III and IV.

A Rectangular Corral with a Total Area of 60 Square