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

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.

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step-by-step explanation: