I. Solve the following problems as indicated. $(5$ points per exercise$)$

$1.$ Mutts Amazing Dogs has developed the following demand forecast for The Pitbull, a spicy concoction graced by pepperjack cheese, serrano, habanero, poblano and jalapeno peppers, onion, and a cilantro$-$lime aioli. They enter the planning period with $20$ hotdogs in inventory as shown in Week $0.$ A few customers have standing orders for hotdogs and they have booked catering events over the next two months.

$\backslash$begin$\{$tabular$\}\{|$c$|$c$|$c$|$c$|$c$|$c$|$c$|$c$|$c$|$c$|\}$

$\backslash$hline Week & $0$ & $1$ & $2$ & $3$ & $4$ & $5$ & $6$ & $7$ & $8\backslash \backslash$

$\backslash$hline Forecast & & $70$ & $80$ & $90$ & $100$ & $120$ & $140$ & $170$ & $220\backslash \backslash$

$\backslash$hline $\backslash$begin$\{$tabular$\}\{$c$\}$

Customer $\backslash \backslash$

Orders

$\backslash$end$\{$tabular$\}$ & & $80$ & $50$ & $30$ & $10$ & $0$ & $0$ & $0$ & $0\backslash \backslash$

$\backslash$hline $\backslash$begin$\{$tabular$\}\{$c$\}$

Projected on$-\backslash \backslash$

hand inventory

$\backslash$end$\{$tabular$\}$ & $20$ & & & & & & & & $\backslash \backslash$

$\backslash$hline MPS & & & & & & & & & $\backslash \backslash$

$\backslash$hline ATP & & & & & & & & & $\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$

a$)$ Perform the necessary calculations to fill out the previous table

b$)$ What should the MPS quantity be for week $3?$

c$)$ What is their available to promise inventory for week $2?$