Crookshanks
New member
- Joined
- May 29, 2005
- Messages
- 10
I'm stuck on question 2 of this problem:
A cook is puzzling over the number of pounds of food he should purchase in order to minimize his cost. He has always bought his food from a small health food store in town. The store sells two types of mixtures. Both of these mixtures contain the three ingredients needed, but the cook needs his own special ratio of these ingredients to meet the requirements of a certain diet. The chart below shows that the diet is to be made up of at least 9 grams of Vitamin B-12, at least 30 grams of calcium, and at least 24 grams of iron. As the chart also shows the ratios for each of the three ingredients in the two mixtures the store sells is not the same as what the cook needs. The cook wants to minimize his costs, and have the minimum requirements met once he combines the two mixtures and cooks up the entire blend.
Dietary Constraints
Vitamin B-12 Calcium Iron
Min. Reqs 9 grams 30 grams 24 grams
Mixture A
= $3.00/lb 1 g per pound 6 g per pound 8 g per pound
Mixture B
= $5.00/lb 3 g per pound 5 g per pound 3 g per pound
Question 1: First set up an equation for the total cost the cook will have to pay for the two mixtures he will buy. This will be called the cost function. Let x = the number of pounds of Mixture A, and y = the number of pounds of Mixture B.
My answer: F(c) = 3x + 5y
Question 2:Next, develop three inequalities utilizing the cook's dietary constraints.
THIS IS WHERE IM STUCK
I came up with
3x + 1y > 9
6x + 5y > 30
8x + 3y > 24
but these don't seem right. I think the (3g per pound, 5g per pound, etc.. is confusing it for me) What am I missing here? Thanks.
A cook is puzzling over the number of pounds of food he should purchase in order to minimize his cost. He has always bought his food from a small health food store in town. The store sells two types of mixtures. Both of these mixtures contain the three ingredients needed, but the cook needs his own special ratio of these ingredients to meet the requirements of a certain diet. The chart below shows that the diet is to be made up of at least 9 grams of Vitamin B-12, at least 30 grams of calcium, and at least 24 grams of iron. As the chart also shows the ratios for each of the three ingredients in the two mixtures the store sells is not the same as what the cook needs. The cook wants to minimize his costs, and have the minimum requirements met once he combines the two mixtures and cooks up the entire blend.
Dietary Constraints
Vitamin B-12 Calcium Iron
Min. Reqs 9 grams 30 grams 24 grams
Mixture A
= $3.00/lb 1 g per pound 6 g per pound 8 g per pound
Mixture B
= $5.00/lb 3 g per pound 5 g per pound 3 g per pound
Question 1: First set up an equation for the total cost the cook will have to pay for the two mixtures he will buy. This will be called the cost function. Let x = the number of pounds of Mixture A, and y = the number of pounds of Mixture B.
My answer: F(c) = 3x + 5y
Question 2:Next, develop three inequalities utilizing the cook's dietary constraints.
THIS IS WHERE IM STUCK
I came up with
3x + 1y > 9
6x + 5y > 30
8x + 3y > 24
but these don't seem right. I think the (3g per pound, 5g per pound, etc.. is confusing it for me) What am I missing here? Thanks.