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Vegfood, a food wholesaler, plans to sell three different nut blends
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18 Apr 2024, 19:28
Plan:
10 servings of 30 gm each
Contain 2 to 4 types of nuts, with none amounting to more than 50% of total cost
AT least 2 of these to be maintained: \(C\leq 10 , P\geq 5 , D\geq 4 , F\leq 3 \)
Ratios
Proportion of nuts in three types of blend is given
Nutrients
Amount of nutrients in 30g of nuts is given
Q.1. Suppose the initial proposals from the Vegfood marketing department concerning proportions of nuts in the blends are followed. For each of the following, select Yes if it gives the weight of pecans that the information provided indicates would be, on average, in a 300 g package of the blend mentioned. Otherwise, select No.
Initial proposal is given under Ratios. Pecans are 0.1, 0.4 and 0.3 in 1 gm of Blend 1, 2 and 3 respectively.
For amount in 300g, multiply the amount by 300, so Pecans will be 0.1*300, 0.4*300 and 0.3*300 in 1*300 gm of Blend 1, 2 and 3 respectively.
That is, 30g, 120g and 90g in Blend 1, 2 and 3 respectively. But the options are 10g, 40g and 90g resp.
So answer is No, No and Yes
Q.2. Suppose Vegfood, after a review of the marketing department's proposal for Blend 1, decided to reconfigure the blend by excluding almonds while making no changes to the 300 g package weight or to the ratios, by weight, among the other types of nuts. Given the information provided, which one of the following must then be true of the reconfigured blend?
Blend 1 had 0.4 or 40% Almonds that will now get distributed in remaining nuts in the ratio of 0.2:0.1:0.3 or 2:1:3
We can calculate each nutrient, which will be time consuming but scanning the graph would give us answer quickly.
(a) The blend's protein content is at least as much as that of the originally proposed Blend 1.
Almond had 6g of protein. But after replacement, the proportion of protein in other nuts is below 6.
Not true
(b) The blend violates the nutritional-profile condition for carbohydrate.
\(C\leq 10\).
If we look at carbohydrates column, the maximum is 9.6g in 30g in Cashew. Thus it would never be more than 9.6g
Does not violate so not true
(c) The blend violates the nutritional-profile condition for dietary fiber.
\(D\geq 4\).
If we look at Dietary fibre column, the maximum is 4g in 30g of Almonds. But Almond is replaced with other nuts containing much lesser amount. Thus it would be lesser than 4g
Does violate, so true
We can check remaining two options too similarly. But we already have our answer above.
(d) The blend violates the nutritional-profile condition for saturated fat.
(e) The blend's saturated-fat content derived from walnuts is no greater than that of the originally proposed Blend 1.
Q.3. Suppose Blend 2 complies with the initial proposals of Vegfood's marketing department. For each of the statements concerning average nutritional content of a 30 g serving of Blend 2, select Yes if the information provided indicates that the statement is correct. Otherwise, select No.
Scan the graph again.
(a) The highest possible proportion of carbohydrate is 9.6g, so it is always less than 10g...Yes
(b) The highest possible proportion of protein is 6g, so it would be 6g, if it contained only almonds. But other nuts have lesser proportion, so overall it is always less than 6g....Yes
(c) The highest possible proportion of dietary fibre is 4g, so it would be 4g, if it contained only almonds. But other nuts have lesser proportion, so overall it is always less than 4g....Yes