Question

A diet is to contain at least 3640 mg vitamin C, 2190 mg Calcium, and 2170 calories every day. Two foods, a dairy-based meal and a vegan option are to fulfill these requirements. Each ounce of the dairy-based meal provides 40 mg vitamin C, 30 mg Calcium, and 10 calories. Each ounce of the vegan option provides 60 mg vitamin C, 30 mg Calcium, and 50 calories. If the dairy-based meal costs $0.21 per ounce and the vegan option costs $0.27 per ounce.
Required:
a. How many ounces of each food should be purchased to minimize costs?
b. What is that minimum cost (per day)?

Answer 1

Answer:

(A) 73 ounces of diary-based meal and 28.8 ounces of the vegan option.

(B) The minimum cost per day is [73 × 0.21] + [28.8 × 0.27] = 15.33 + 7.776 = $23.106

Explanation:

First thing to note is that the dairy-based meal costs less than the vegan option. In otherwords, if you're to minimize cost, you should purchase as many ounces of dairy-based meal as possible. This is the first mindset or step.

What the diet should contain everyday:

3640mg - Vitamin C

2190mg - Calcium

2170 - Calories

DAIRY BASED:

(40 × 91 = 3640), (30 × 73 = 2190), (10 × 217 = 2170)

VEGAN OPTION:

(60 × 60.67 = 3640), (30 × 73 = 2190), (50 × 43.4 = 2170)

Getting 73 ounces of dairy-based meal, you have

(40 × 73), (30 × 73), (10 × 73) = 2920mg, 2190mg, 730 calories.

You have left 720mg of Vitamin C and 1440 calories to obtain from the Vegan Option.

(60 × 12 = 720), (30 × 0 = 0), (50 × 28.8 = 1440)

The highest quantity needed here is 28.8 ounces of calories from the vegan option, hence 28.8 ounces of the vegan meal should be purchased. There will be excesses of Vitamin C and Calcium but that is necessary in order to purchase the stipulated minimum amount of each nutrient.

The minimum cost per day will now be [73 × 0.21] + [28.8 × 0.27] = 15.33 + 7.776 = $23.106