Danish is working with Amazing Paints $($AP$),$ a paint manufacturing company

having their plant in Kasur and major DC in Lahore. They are producing $200$

Gallons a day to fulfill demand, but their plant has a capacity of $500$ Gallons a

day. They make $8$ types of paints. They make $6$ paints in $8$ colors and $2$ paints

in $10$ colors. Danish asked for the rationale of production volume set to $200$

Gallons per day. The supervisor mentioned that this is the standard production

for the last $5$ years. Danish has carried out demand survey and has estimated

that the demand is way more than $200$ Gallons per day $($about $390$ Gallons$/$day$)$

for their customer base and company is losing revenues. Their landed cost of on

SKU of paint is Rs$.1600/$ Gallon and they sell at the very competitive rate of Rs$.$

$4400/$ Gallon. Major brands like Master Paints, ICI paints, and Berger Paints

sell within a range of $9000-15000/$ Gallon. They are other local brands which

are selling at about $6000-8000/$ Gallon. After running the plant at production

level, he collected data for $10$ day which is given as follows in tabular form.$($Both the demand

and forecasts are in gallons$).$

Day Xt a$^$t b$^$t X$^$t$,$t$+1$ MSE

$0386$

$1416$

$2408$

$3418$

$4406$

$5418$

$6420$

$7416$

$8422422\mathrm{.}822\mathrm{.}49????24\mathrm{.}39$

$9432????????????????$

$10430????????????????$ Danish has then decided to use Holt$$s model for forecasting at this point. Initial

parameters a & b and smoothing constants $(\backslash$alpha $,\backslash$beta & $\backslash$omega $)$ have been carefully

selected. Where, $\backslash$alpha $=0\mathrm{.}25,\backslash$beta $=0\mathrm{.}15,\backslash$omega $=0\mathrm{.}07$

$1.$ How much potential Profit the company is losing on a daily basis with their

current production $(200$ Gallons$/$day$)?$