in order to grow a certain crop, it is recommended that each square foot of ground be treated with 10 units of phosphorous, 9 units of potassium, and 19 units of nitrogen, suppose that there are three brands of fertilizer on the market - say brand X, brand Y, and brand Z. One pound of brand X contains 1 unit of phosphorous, 3 units of potassium, and 4 units of nitrogen. One pound of brand Z contains only 1 unit of phosphorous and 1 unit of nitrogen.
a. Determine whether or not possible to meet exactly the recommendation by applying some combination of three brands of fertilizer. Give your reasoning.
b. if it is possible to meet the recommendation, what is the combination of the three brands that satisfies the recommendation?
i domt know
a. To determine whether it is possible to meet the recommendation by applying a combination of the three brands of fertilizer, we will check if the combination of the nutrients in each brand can satisfy the recommended amount for each nutrient.
Let's calculate the nutrient content per pound for each brand:
- Brand X: 1 unit of phosphorous, 3 units of potassium, and 4 units of nitrogen.
- Brand Y: Nutrient content is not specified.
- Brand Z: 1 unit of phosphorous and 1 unit of nitrogen.
Now, let's check if the combination of the three brands can fulfill the recommended amount for each nutrient:
Phosphorous: The recommended amount is 10 units per square foot. Brand X provides 1 unit of phosphorous per pound, so 10/1 = 10 pounds of Brand X would be required. Brand Z also provides 1 unit of phosphorous per pound, so 10/1 = 10 pounds of Brand Z would be required. Since there is no information about the nutrient content of Brand Y, we cannot determine if it can contribute to the recommended amount of phosphorous.
Potassium: The recommended amount is 9 units per square foot. Brand X provides 3 units of potassium per pound, so 9/3 = 3 pounds of Brand X would be required. Since there is no information about the nutrient content of Brand Y, we cannot determine if it can contribute to the recommended amount of potassium.
Nitrogen: The recommended amount is 19 units per square foot. Brand X provides 4 units of nitrogen per pound, so 19/4 = 4.75 pounds of Brand X would be required. Brand Z provides 1 unit of nitrogen per pound, so 19/1 = 19 pounds of Brand Z would be required. Since there is no information about the nutrient content of Brand Y, we cannot determine if it can contribute to the recommended amount of nitrogen.
Based on the information given, we can conclude that it is not possible to meet exactly the recommendation by applying a combination of the three brands of fertilizer, as there is no information about the nutrient content of Brand Y.
b. Since it is not possible to meet the recommendation exactly, we cannot determine the combination of the three brands that would satisfy the recommendation.