Asmall organic food store makes two types of fruit smoothies: tropical and sport. each tropical smoothie uses 9 oz of orange juice and 6 oz of milk. each sport smoothie uses 3 oz of orange juice and 3 oz of milk. the store stores the orange juice in a 210-oz container and milk in an 150-oz container. the store sells the tropical smoothies for $4 and sells the sport smoothie for $3. what is the maximum in sales the store can make from 1 container each of orange juice and milk? $100 $110 $150 $280

The Z is maximum when he sells 50 units of sport smoothie  and cost is $150.

Step-by-step explanation:

Let  x denotes the total number of  tropical smoothie

and y denotes  the total number of  sport smoothie

Attachment  shows the data given

Given : The store stores the orange juice in a 210-oz container and milk in an 150-oz container.

To make both smoothies total orange juice is given as

For tropical smoothie 9x

and for sport smoothie 3y

then  9x + 3y ≤ 210

Simplify, we get,

3x + y ≤ 70  

To make both smoothies total milk is given as

For tropical smoothie 6x

and for sport smoothie 3y

then  6x + 3y ≤ 150

Simplify, we get,  

2x + y ≤ 50  

We have to maximize the sales.

That is Max Z = 4x + 3y

Thus, the constraints are,

3x + y ≤ 70  

2x + y ≤ 50  

x ≥ 0

y ≥ 0

Plotting these equation on graph , we obtained the graph as shown below.

We find the points for feasible region, that is the point that satisfy the both the inequality.

Thus, the points are (0,50) , (20,10) and (23.33,0)

We find the value of Z = 4x + 3y on the above points (as show in image attached)

Thus, the Z is maximum when he sells 50 units of sport smoothie  and cost is $150.

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