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A little kid running a lemonade stand sells small and large beverages. Each small beverage sells for $2 and each large beverage sells for $5. Small beverages require 4 lemons and 6 tablespoons of sugar each. Large beverages require 5 lemons and 10 tablespoons of sugar each. She has 100 lemons and 180 tablespoons of sugar. How many of each beverage should she sell to maximize her earnings?

Respuesta :

hamzaahmeds

Answer:

No. of Small Beverage = x = 10

No. of Large Beverage = y = 12

Step-by-step explanation:

Analyzing the given situation, we can form two algebraic equations.

Since, she has 100 lemons and 4 lemons are required for small beverage, while 5 lemons are required for large beverage. So, we can form the equation:

4x + 5y = 100   --------- eqn (1)

where,

x = No. of small beverages sold

y = No. of large beverages sold

Similarly, she has 180 table spoons of sugar and 6 table spoons are required for small beverage, while 10 table spoons are required for large beverage. So, we can form the equation:

6x + 10y = 180   -------- eqn (2)

From eqn (1):

x = (100 - 5y)/4   ------- eqn (3)

Substituting this value of x in eqn (2)

(6)(100 - 5y)/4 + 10y = 180

10 y - 7.5 y= 180 - 150

2.5 y = 30

y = 30/2.5

y = 12

Using this value of y in eqn (3)

x = [100 - (5)(12)]/4

x = 10

Therefore, in order to maximize the earnings the kid should sell following number of each beverage:

No. of Small Beverage = x = 10

No. of Large Beverage = y = 12

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