Pick some smart number for \(x\), let \(x=2\) (I chose \(x=2\) as in this case monthly shipments would be \(\frac{x}{2}=1\)).

From November to February \(4x=8\) rakes were produced and in March business paid for storage of 8-1=7 rakes, in next month for storage of 6 and so on.

So total storage cost would be: \(0.1(7+6+5+4+3+2+1)=2.8\) --> as \(x=2\), then \(2.8=1.4x\).

Answer: C.
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x + x + x + x -> rakes produced

x/2 * 8 -> Rakes exported


Storage cost =

7x/2 * 0.1 + 3x + 0.1 + 5x/2 * 0.1 + 2x * 0.1 + 3x/2 * 0.1 + x * 0.1 + x/2 * 0.1

( 3.5 + 3 + 2.5 + 2 + 1.5 + 1 + 0.5)x * 0.1

Answer - C
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the costs are = 7x/2 +5x/2+3x/2+x/2+3x+3x+x = 14x
14x * 0.1 = 1.4x

Picking smart numbers is an easy and smart solution here. Here's algebra as well:

4x rakes are produced, x/2 are sold each month, and we're assuming at the beginning of each month.

So storage costs
= .1((4x-x/2)+(4x-2x/2)+(4x-3x/2)+(4x-4x/2)+(4x-5x/2)+(4x-6x/2)+(4x-7x/2)+(4x-8x/2))
= .1(8*4x-36x/2)
= .1(32x-18x)
= .1(14x)
= 1.4x

Let \(x=2\):

The business produced x rakes each month from November through February --> from November to February \(4x=8\) rakes were produced.
The business shipped x/2 rakes, so 1 rake, at the beginning of March and started paying storage costs in March, so in March business paid for storage of 8-1=7 rakes.

Please re-read the question and the solutions above.

Similar question to practice: the-acme-company-manufactured-x-brooms-per-month-from-januar-144318.html
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You can solve this one using 3 Methods

Method 1
Number picking (see Bunuel's approach)

Method 2
Brute force; Just list the number of monats shipments etc.

Month......1.....2....3........4......5......6.......7.....8
Storage...3,5...3....2,5.....2.....1,5....1......0,5...0 Rakes
Costs....0,35..0,3...0,25..0,2...0,15..0,1...0,05..0 --> 1,4x

Method 3
Number of terms * Average = 7*2=14
14*0,1=1,4
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Explanation:

Given certain business produced x rakes each month from November through February and shipped x/2 rakes at the beginning of each month from March through October.

From November to February, i.e. in 4 months, x rakes each month are produced.
⇒ Total number of racks produced = 4x

Also given the business paid no storage costs for the rakes from November through February, but it paid storage costs of $0.10 per rake each month from March through October for the rakes that had not been shipped.

From March to October, i.e. in 8 months, x/2 rakes each month are shipped. Hence, from March onwards, number of rakes decreases by x/2 at the beginning of every month.

Total storage cost in 12 months
= Storage cost from Nov. to Feb. + storage cost from March to Oct.
= 0 + storage cost from March to Oct.

Number of racks remaining in March = 4x − x/2 = 7x/2. Similarly number of racks remaining from April through September will be 3x, 5x/2, 2x, 3x/2, x and x/2.

Total storage cost from March to Oct. = 0.10 (7x/2 + 3x + 5x/2 + 2x + 3x/2 + x + x/2) = 1.40x

Answer: C.