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# A company sells seed either by the pound or by the acreage planted.

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Joined: 14 Oct 2012
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A company sells seed either by the pound or by the acreage planted.  [#permalink]

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15 Nov 2017, 18:13
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Difficulty:

85% (hard)

Question Stats:

43% (03:15) correct 57% (03:16) wrong based on 37 sessions

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A company sells seed either by the pound or by the acreage planted. It will sell seed M for no less than \$5.50 a pound or for no less than \$12.75 per acre planted. Farmers will pay no more than \$6.25 a pound and no more than \$13.50 per acre planted and always choose the price structure that results in the lowest cost per acre. If it takes 2 pounds of seed M to plant an acre of loamy soil and 3 pounds to plant an acre of clay soil, what is the range in dollars per pound, x, within which sales of seed M could take place?

(A) \$4.25 ≤x ≤ \$5.50
(B) \$4.25 ≤x ≤ \$6.25
(C) \$4.50 ≤x ≤ \$6.25
(D) \$5.50 ≤x ≤ \$6.75
(E) \$5.50 ≤x ≤ \$13.50
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Joined: 02 Aug 2009
Posts: 7971
Re: A company sells seed either by the pound or by the acreage planted.  [#permalink]

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15 Nov 2017, 19:23
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manishtank1988 wrote:
A company sells seed either by the pound or by the acreage planted. It will sell seed M for no less than \$5.50 a pound or for no less than \$12.75 per acre planted. Farmers will pay no more than \$6.25 a pound and no more than \$13.50 per acre planted and always choose the price structure that results in the lowest cost per acre. If it takes 2 pounds of seed M to plant an acre of loamy soil and 3 pounds to plant an acre of clay soil, what is the range in dollars per pound, x, within which sales of seed M could take place?

(A) \$4.25 ≤x ≤ \$5.50
(B) \$4.25 ≤x ≤ \$6.25
(C) \$4.50 ≤x ≤ \$6.25
(D) \$5.50 ≤x ≤ \$6.75
(E) \$5.50 ≤x ≤ \$13.50

Hi..

We have to find the lowest and max for the range..
Company -
5.5 per pound or 12.75 per acre
But 3 pounds are required for claysoil per acre, so price per pound if someone pays by acre =12.75/3=4.25
So lowest is 4.25

Farmer
6.25 pound or 13.50 if paid per acre..
Since we are looking for higher range, say he buys 2 pounds for loamy soil.
13.50/2=6.75 BUT he will always choose what costs the least per acre, so buying 2 pounds at 6.25= 2*6.25=12.50 will be cheaper than buying per acre.
13.5 for 3 pounds will ofcourse be <6.25
So higher range will remain 6.25 only

So lowest when company sells per acre for claysoil =4.25
Highest when farmer buys per pound for loamy soil = 6.25

So range should be \$4.25 ≤x ≤ \$6.25

B
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Re: A company sells seed either by the pound or by the acreage planted.  [#permalink]

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20 Feb 2019, 16:41
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Re: A company sells seed either by the pound or by the acreage planted.   [#permalink] 20 Feb 2019, 16:41
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