12. –/7.14 points WaneFMAC7 6.2.025.My Notes You manage an ice cream factory tha

Question

12.–/7.14 pointsWaneFMAC7 6.2.025.My Notes

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 550 eggs and 900 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?

Explanation / Answer

Since the vanilla is most profitable, you make as much of it as possible subject to the constraints on the ingredients and to maximize the total profit. So

Let x = #quarts of creamy vanilla ice cream

y = #quarts of continental mocha ice cream

P = total profit of all the ice cream made

Ingredient constraints are:

Eggs used = 2x + 1y <= 550. note that x cannot exceed 275 because that will use up all the eggs

Cream used = 3x + 3y<= 900 cups, therefore, x + y <=300 quarts

Profit P = 3x + 2y in dollars

Solve both equations we get

x = 250 and y = 50

So x = 250 and y = 50 maximizes the ice cream profit at $850   

Hope this will be helpful. Thanks and God Bless You :-)

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