The ACME company - PS

[GMAT_ClubMBA]

The ACME company manufactured x brooms per month from January to April, inclusive. On the first of each month, during the following May to December, inclusive, it sold x/2 brooms. At the beginning of production on January 1st, the ACME company had no brooms in its inventory. If storage costs were $1 per month per broom, approximately how much, in terms of x, did the ACME company pay for storage from May 2nd to December 31st, inclusive?
$x
$3x
$4x
$5x
$14x

Respuesta:

respuesta: show

E

[ncp]

respuesta: show

A 1 de Mayo tendremos 4X brooms
A 31 de Diciembre quedarán 0 debido a 4X - \frac{8X}{2}[/m]

A 2 de Mayo ya se ha vendido el primer lote de \frac{X}{2}[/m] brooms por lo que durante dicho mes almacenaremos \frac{7X}{2}[/m]
Así en adelante todos los meses \frac{6X}{2}[/m], \frac{5X}{2}[/m], \frac{4X}{2}[/m], ... hasta 0 en Diciembre.

Sabiendo que el coste es 1 para cada mes, el coste total es la suma de todos los brooms que almacenamos que es 14X

Respuesta E

[Tradewind]

The ACME company manufactured x brooms per month from January to April, inclusive. On the first of each month, during the following May to December, inclusive, it sold x/2 brooms. At the beginning of production on January 1st, the ACME company had no brooms in its inventory. If storage costs were $1 per month per broom, approximately how much, in terms of x, did the ACME company pay for storage from May 2nd to December 31st, inclusive?
$x
$3x
$4x
$5x
$14x

Respuesta:

respuesta: show

E

X brooms per month during 4 months = 4X brooms.

Sold X/2 brooms for 8 months, so inventory left at the end was 0.

I'd solve this the "easy way". Quick chart with 12 months and the production vs. inventory results from sales:

Month | Production | Sales
J_________X_________X
F________2X________2X
M________3X________3X
A________4X________4X
M_________________3,5X
J_________________3,0X
J_________________2,5X
A_________________2,0X
S_________________1,5X
O_________________1,0X
N_________________0,5X
D_________________0,0X

Total inventory supported for the last 8 months:

Answer E.