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A food manufacturer has created four prototypes of a new product to be launched next year. Each prototype contains three main ingredients—fruit, wheat flour, and chocolate—in varying proportions, as shown in the first graph. The cost per pound (Price/lb) for each ingredient is shown in the second graph.
From each drop-down menu, select the option that creates the most accurate statement according to the information provided.
Assuming that all prototypes weigh the same, the product with the lowest total cost per unit is , with a per-pound product cost of .
A food manufacturer has created four prototypes of a new product to be launched next year. Each prototype contains three main ingredients—fruit, wheat flour, and chocolate—in varying proportions, as shown in the first graph. The cost per pound (Price/lb) for each ingredient is shown in the second graph.
From each drop-down menu, select the option that creates the most accurate statement according to the information provided.
Assuming that all prototypes weigh the same, the product with the lowest total cost per unit is , with a per-pound product cost of .
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Looking at the second chart, we see that Wheat is the cheapest ingredient, while Chocolate is the most expensive. Since all products weigh the same, it’s reasonable to assume that the cheapest product will be the one that uses the highest percentage of Wheat and the lowest percentage of Chocolate. This is our initial assumption going into the question.
From the first graph, we can identify that Prototype C fits this pattern—it contains 50% Wheat and only 10% Chocolate, making it the likely cheapest product. There’s no need to calculate the exact cost to determine the answer or compare the other prototypes.
For the second dropdown, however, we do need the exact cost of the cheapest product.
Calculating the cost for Prototype C, we get: 0.4 * 20 + 0.5 * 10 + 0.1 * 40 = 17.
Hey, Shouldnt the answer for dropdown 1 be 'protoype D'? as that one represent the composition of "0.4x20 + 0.5x10 + 0.1x40 = 17"
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Official Solution:
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A food manufacturer has created four prototypes of a new product to be launched next year. Each prototype contains three main ingredients—fruit, wheat flour, and chocolate—in varying proportions, as shown in the first graph. The cost per pound for each ingredient is shown in the second graph.
From each drop-down menu, select the option that creates the most accurate statement according to the information provided.
Assuming that all prototypes weigh the same, the product with the lowest total cost per product is with the per pound product cost of .
Looking at the second chart, we see that Wheat is the cheapest and Chocolate is the most expensive ingredients. Since all products weigh the same, chances are pretty good that the cheapest product will be the one that uses the most of the Wheat and the least Chocolate. That's our assumption going into the question.
From the first Graph, we can spot that Prototype C fits this pattern - it has 50% Wheat and only 10% Chocolate. This will be the cheapest product. There is no need to calculate the exact cost to be able to answer this question or to compare them.
For the second drop down, we do need the exact cost of the cheapest product. Calculating the cost, we get: 0.4x20 + 0.5x10 + 0.1x40 = 17
Hey, Shouldnt the answer for dropdown 1 be 'protoype D'? as that one represent the composition of "0.4x20 + 0.5x10 + 0.1x40 = 17"
Show more
No, the answer for dropdown 1 should be Prototype C, not Prototype D. It seems you’re mixing up the percentages of Chocolate and Fruit. Prototype D contains 40% Chocolate, 50% Wheat, and 10% Fruit, whereas Prototype C contains 10% Chocolate, 50% Wheat, and 40% Fruit. Since Chocolate is the most expensive ingredient, and Prototype C has the lowest percentage of it, Prototype C results in the lowest cost, which is why it’s the correct answer.
A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.