13 cents for A 12 cents for B. total protein greater than twelve grams. Total fat less than eight grams. Total grams less than thirty five grams. .5 grams protein and .3 grams fat for A. .6 grams protein and .2 grams fat for B. what is optimal cost
To find the optimal cost, we need to compare the cost of each item while considering the given criteria. Let's break down the information provided:
Item A:
- Cost: 13 cents
- Protein: 0.5 grams
- Fat: 0.3 grams
Item B:
- Cost: 12 cents
- Protein: 0.6 grams
- Fat: 0.2 grams
Criteria:
- Total protein must be greater than 12 grams.
- Total fat must be less than 8 grams.
- Total grams must be less than 35 grams.
Now, let's calculate the maximum number of items we can purchase within those constraints:
For protein:
12 grams / 0.5 grams (protein per Item A) = 24 items
For fat:
8 grams / 0.3 grams (fat per Item A) = 26.67 (approximately) items
Since we can't purchase a fraction of an item, we need to consider the maximum number of whole items we can buy. We'll multiply the fractional part with the respective cost to determine the cost of the last item.
For protein:
0.67 (fractional part) * 13 cents (cost of Item A) = 8.71 cents
For fat:
0.67 (fractional part) * 13 cents (cost of Item A) = 8.04 cents
Now, let's compare the costs:
Cost of 24 items of A: 24 * 13 = 312 cents
Cost of 25th Item A: 8.71 cents
Total cost for A: 312 + 8.71 = 320.71 cents
Cost of 26 items of A: 26 * 13 = 338 cents
Cost of 27th Item A: 8.71 cents
Total cost for A: 338 + 8.71 = 346.71 cents
Cost of 26 items of B: 26 * 12 = 312 cents
Cost of 27th Item B: 12 cents
Total cost for B: 312 + 12 = 324 cents
Therefore, the optimal cost would be to purchase 26 items of item B for a total cost of 324 cents.