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  • Directions for question : At the Happily Tipsy Bar, the chief bar-tender, after a lot of experimentation found out t

Directions for question :

At the Happily Tipsy Bar, the chief bar-tender, after a lot of experimentation found out that Vodka, White Rum, Gin and Tequila if mixed in different concentrations can create four very exciting cocktails which he named as the Teqnical, the Hard Haddock, the Fiery Ginie and the Russian Heat. The respective percentage alcohol concentrations of the cocktails are provided in the chart below. 

He priced them at Rs 160, Rs 400, Rs 320 and Rs 240 per single peg respectively. On specific orders from customers, he was ready to mix two or more drinks in the ratio as fancied by the customer.

Alcohol Vodka White Rum Gin Tequila
Cocktail
TEQNICAL 18 32 8 42
HARD HADDOCK 8 42 32 18
FIERY GINIE 9 27 37 27
RUSSIAN HEAT 42 13 37 8

Question :

On the 31st March of a particular year, the management of Happily Tipsy Bar wanted to finish off their inventory as much as possible, as the remnant of the inventory would be destroyed. On checking they found that 14.7 liters of Vodka purchased @ Rs 300 per liter, 76.8 liters of White Rum purchased @ Rs 550 per liter, 58.6 liters of Gin purchased @ Rs 500 per liter and 33 liters of Tequila purchased @ Rs 400 per liter were there as inventory. Assuming that there would be no mixing of cocktails to be served to any customer on that day, and that the maximum possible inventory got exhausted, what could be the maximum profit that could be made (in lakhs of Rs rounded to the first decimal place) on the sales of cocktails made from the inventory on 31st March at Happily Tipsy Bar, neglecting all other expenses ? (One peg = 60ml)

Option: 1

12.2    


Option: 2

11.3    


Option: 3

9.4


Option: 4

8.5


Answers (1)

best_answer

Inventory and cost of inventory on 31st March of a particular year at Happily Tipsy Bar :

Vodka : 14.7 liters (14700 ml) @ Rs 300/lit, that is Rs (14.7*300) = Rs 4410,

White Rum : 76.8 liters (76800 ml) @ Rs 550/lit, that is Rs (76.8*550) = Rs 42240,

Gin : 58.6 liters (58600 ml) @ Rs 500/lit, that is Rs (58.6*500) = Rs 29300,

Tequila : 33 liters (33000 ml) @ Rs 400/lit, that is Rs (33*400) = Rs 13200.

Total cost of inventory = Rs (4410+42240+29300+13200) = Rs 89,150

Since the target is to make maximum profit, hence the cocktail costing the highest, that is Hard Haddock, has to be targeted first, especially because we can also see on inspection that the distribution of the inventory is in approximate sync to the concentration of Vodka, White Rum Gin and Tequila in Hard Haddock.

Quantity present per peg (60 ml) of Hard Haddock :

Vodka : (8*60)/100 = 4.8 ml

White Rum : (42*60)/100 = 25.2 ml

Gin : (32*60)/100 = 19.2 ml, and

Tequila : (18*6)/100 = 10.8 ml

Quotient of 14700/4.8 = 3062

Quotient of 76800/25.2 = 3047

Quotient of 58600/19.2 = 3052

Quotient of 33000/10.8 = 3055

The minimum quotient will ensure the number of pegs of Hard Haddock that can be served to the customers on 31st March at Happily Tipsy Bar, that is 3047 pegs.

Quantity left after serving 3047 pegs of Hard Haddock :

Vodka : 14700 – (4.8*3047) = (14700 – 14625.6) = 74.4 ml

White Rum : 76800 – (25.2*3047) = (76800 – 76784.4) = 15.6 ml 

Gin : 58600 – (19.2*3047) = (58600 – 58502.4) = 97.6 ml, and 

Tequila : 33000 – (10.8*3047) = (33000 – 32907.6) = 92.4 ml.

White Rum content left is the minimum, and so we should target the cocktail that uses minimum concentration of White Rum, that is Russian Heat. 

Quantity present per peg (60 ml) of Russian Heat :

Vodka : (42*60)/100 = 25.8 ml

White Rum : (13*60)/100 = 7.8 ml

Gin : (37*60)/100 = 22.2 ml, and

Tequila : (8*6)/100 = 4.8 ml

Quotient of 74.4/25.8 = 2

Quotient of 15.6/7.8 = 2

Quotient of 97.6/22.2 = 4

Quotient of 92.4/4.8 = 19

The minimum quotient will ensure the number of pegs of Russian Heat that can be served to the customers on 31st March at Happily Tipsy Bar, that is 2 pegs.

Quantity left after serving 2 pegs of Russian Heat :

Vodka : 74.4 – (25.8*2) = (74.4 – 51.6) = 22.8 ml

White Rum : 15.6 – (7.8*2) = (15.6 – 15.6) = 0 

Gin : 97.6 – (22.2*2) = (97.6 – 44.4) = 53.2 ml, and 

Tequila : 92.4 – (4.8*2) = (92.4 – 9.6) = 82.8 ml.

The above quantity got destroyed.

Hence income from serving 3047 pegs of Hard Haddock and 2 pegs of Russian Heat 

= Rs (3047*400 + 2*240)

= Rs (1218800 + 480)

= Rs 12,19,280

Hence profit made on 31st March at the Happily Tipsy Bar on the sales of cocktails made from the inventory, neglecting all other expenses

= Rs (1219280 – 89150)

= Rs 11,30,130, 

that is Rs 11.3 lakhs

Posted by

Gaurav

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