Q$\mathrm{.}2$ Thendral Krishnan $($TK$)$ is the co$-$founder and CEO of Great Western Vineyard $($GWV$),$ a vineyard established in Thekkady, Kerala. GWV cultivates three types of grapes, namely, $($a$)$ Malbec, $($b$)$ Cabernet, and $($c$)$ Riesling. The monthly production of Malbec, Cabernet, and Riesling at GWV is $350$ kg$,300$ kg$,$ and $200$ kg$,$ respectively. Using these grapes, Thendral Krishnan makes three brands of wines, namely, $($a$)$ Chardonnay, $($b$)$ Blanc, and $($c$)$ Riesling W$.$ The wines are made by mixing the three different types of grapes and two additives at various proportions. The amount of grapes and additives used to produce one litre of different brands of wines are shown in table: The profit earned from wines Chardonnay, Blanc, and Riesling W is $400,950,$ and $1350$ per $1$ litre, respectively. The following LP formulation is written to maximize the profit. Monthly maximum demand for Chardonnay, Blanc, and Riesling W is $1000,750,$ and $250$ respectively. Let X

$1$

$$

$=$ Amount $($in litres$)$ of Chardonnay produced

X

$2$

$$

$=$ Amount $($in litres$)$ of Blanc produced

X

$3$

$$

$=$ Amount $($in litres$)$ of Riesling W produced

$$

The objective is Max$400$X

$1$

$$

$+950$X

$2$

$$

$+1350$X

$3$

$$

Subject to

$1\mathrm{.}25$X

$1$

$$

$+0\mathrm{.}80$X

$2$

$$

$+0\mathrm{.}40$X

$3$

$$

$0\mathrm{.}75$X

$1$

$$

$+1\mathrm{.}80$X

$2$

$$

$+0\mathrm{.}60$X

$3$

$$

$0\mathrm{.}15$X

$1$

$$

$+0\mathrm{.}25$X

$2$

$$

$+2\mathrm{.}00$X

$3$

$$

$0\mathrm{.}10$X

$1$

$$

$+0\mathrm{.}05$X

$2$

$$

$+0\mathrm{.}08$X

$3$

$$

$0\mathrm{.}20$X

$1$

$$

$+0\mathrm{.}15$X

$2$

$$

$+0\mathrm{.}12$X

$3$

$$

X

$1$

$$

X

$2$

$$

X

$1$

$$

$,$X

$2$

$$

$,$X

$3$

$$

$>=0$

$$

$<=350$

$<=300$

$<=200$

$<=120$

$<=80$

$<=1000$

$<=750$

X

$3$

$$

$<=250$

$$

The sensitivity report output is provided below: Based on the provided information, answer the following questions. a$)$ What is the value of the objective function at optimality? $[$CLO $2,1$ Mark$]$ b$)$ A loyal customer of TK has asked for $20$ litres of Chardonnay wine. What will be the impact on profit for GWV if TK decides to supply Chardonnay wine? TK would like to ensure that supplying Chardonnay will not impact the profitability of GWV$.$ What will be your suggestion? $[$CLO $2,3$ Mark$]$ c$)$ In addition to producing on its own, TK can procure Malbec from Bangalore. Should he procure it$?[$CLO $2,2$ Mark$]$ d$)$ The supplier of Cabernet grapes from Bangalore is ready to provide an additional quantity of $400$Kg as requested for Rs$.480$ per Kg$.$ Should TK buy $400$ kg from Bangalore supplier? Justify your answer. $[$CLO $2,2$ Mark$]$ e$)$ The grape Malbec can be directly sold in market at $70$Rs per kg instead of using them in wine production. What will be your suggestion? If yes, then what quantity of Malbec grape can be sold in market? $[$CLO $2,1$ Mark$]$ f$)$ Due to Reisling crop failure in Nappa county, the demand for Reisling W increases significantly. TK decided to increase profit on Reisling W to $3500$ Rs$.$ What will be the impact on optimal solution? $[$CLO $2,1$ Mark