Helena Lorimer runs a set of ice cream cafes that sell mainly three flavors of i

Question

Helena Lorimer runs a set of ice cream cafes that sell mainly three flavors of ice cream: vanilla, chocolate, and strawberry. Hot weather and high demand have caused her to run short of the main ingredients: milk, sugar, and cream. She has decided to make the best assortment of ice cream quantities in these three flavors and ration out the deliveries to the cafes. She has collected data on the profitability of the various flavors, availability of supplies, and the amounts of ingredients required for each flavor. Flavor Profit per Usage/Gallon Gallon Milk (gal.) Sugar (lbs.) Cream (gal.) $1.00 $0.90 $0.95 Chocolate 0.45 0.50 0.40 200 0.50 0.40 0.40 150 0.10 0.15 0.20 60 anilla Strawberry Max available She wants to determine the optimal product mix for the Lorimer ice cream. Let x1-the # of gallons of Chocolate ice cream made the # of gallons of Vanilla ice cream made the # of gallons of Strawberry ice cream made X2 Max Z = $1.00x1 + $0.90x2 + $0.95x3 Subject To: 0.45x, + 0.50x2 + 0.40x3 s200 gal Mlk Supply Constraint 0.50x, +0.40x2 + 0.40x s,150 lbs Sugar Supply Constraint 0.10x, +0.15x2+ 0.20x 60 gal Cream Supply Constraint 2 0 gallons x, Non-negativity Constraint

Explanation / Answer

solving using excel solver we get

Optimal Solution: p = 341.25; x1 = 0, x2 = 300, x3 = 75

hence

option A) x2 = 3000 is correct

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