Q:

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? HINT (See Example 2.] (If an answer does not exist, enter DNE.) Creamy Vanilla quarts Continental Mocha quarts

Accepted Solution

A:
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 + 2yWhich 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 = 2xCups of cream = 3xAlso, Each quart of Continental Mocha go 1 egg and 3 cups of cream,So, in creamy vanilla, Number of eggs = yCups of cream = 3yThus, total number of eggs = 2x + yAnd, total number of cups of cream = 3x + 3yAccording to the question,2x + y ≤ 3503x + 3y ≤ 600Which 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 = $ 550At ( 175, 0)Z = 3(175) + 2(0) = $ 525Hence, 150 quartz of creamy vanilla and 50 quartz of Continental Mocha should make to earn the largest profit.