Question

You manage an ice cream factory that makes two flavors: Creamy Vanilla and Continental Mocha. Into each quart of Creamy Vanilla go 2 eggs and 3 cups of cream. Into each quart of Continental Mocha go 1 egg and 3 cups of cream. You have in stock 350 eggs and 600 cups of cream. You make a profit of $3 on each quart of Creamy Vanilla and $2 on each quart of Continental Mocha. How many quarts of each flavor should you make to earn the largest profit

Answer 1

Answer:

150 quartz of creamy vanilla and 50 quartz of Continental Mocha.

Step-by-step explanation:

Let x represents the number of quartz of Creamy vanilla and y represents the number of Continental Mocha,

∵ There is a profit of $ 3 on each quart of Creamy Vanilla and $2 on each quart of Continental Mocha.

So, the total profit,

Z = 3x + 2y

Which is the objective function for this problem that has to maximise,

Each quart of Creamy Vanilla go 2 eggs and 3 cups of cream,

So, in creamy vanilla,

Number of eggs = 2x

Cups of cream = 3x

Also, Each quart of Continental Mocha go 1 egg and 3 cups of cream,

So, in creamy vanilla,

Number of eggs = y

Cups of cream = 3y

Thus, total number of eggs = 2x + y

And, total number of cups of cream = 3x + 3y

According to the question,

2x + y ≤ 350

3x + 3y ≤ 600

Which are subject of constraint,

Graphing :

Related equation of 2x + y ≤ 350 is 2x + y = 350,

Having x-intercept = (175,0) y-intercept = (0, 350)

Also, 2(0) + 0 ≤ 350 ( True )

∴ Shaded region of 2x + y ≤ 350 would contain the origin,

Related equation of 3x + 3y ≤ 600 is 3x + 3y = 600,

Having x-intercept = (200,0) y-intercept = (0, 200)

Also, 3(0) + 3(0) ≤ 600 ( True )

∴ Shaded region of 3x + 3y ≤ 600 would contain the origin,

'≤' shows solid line,

By graphing them we obtain a feasible region,

In which boundary points are (0, 200), (150, 50) and (175,0)

At (0, 200),

Z = 3(0) + 2(200) = $ 400,

At ( 150, 50)

Z = 3(150) + 2(50) = 450 + 100 = $ 550

At ( 175, 0)

Z = 3(175) + 2(0) = $ 525

Hence, 150 quartz of creamy vanilla and 50 quartz of Continental Mocha should make to earn the largest profit.