Question

Consider the following problem faced by a Dietician:

A diet needs to be created that contains not less than 1713 calories, not more than 52 grams of protein, not less than 18 grams of carbohydrates and not less than 14 grams of fat. Also, the diet should have minimal cost. In addition the diet should include at least 1.9 Units of fish and at least 1cup of milk.

The diet will consist of the six different foods: Bread, Milk, Cheese, Fish, Potato and Yogurt. The following table lists the cost per unit of each item and the number of grams of protein, fat, and carbohydrates per unit as well as the calories that will be supplied by each food unit.

	Bread	Milk	Cheese	Potato	Fish	Yogurt
Cost, (cents)	10	35	28	11	72	22
Protein, g	4	11	7	1.3	10	10.2
Fat, g	2	7	13	0.1	9	3
Carbohydrates, g	21	15.7	0.4	39.6	0	20
Calories, Cal	145	142	138	124	196	304

Find a diet that meets the requirements above while keeping the cost at an absolute minimum. Make sure that your Food Units are all Integers.

Minimum Cost =

(Cents) Hint: Min Cost value is between 264 and 282

Number of Units of Each Item … Make sure your answers are INTEGERS


Bread =

Milk=

Cheese=

Potato=

Fish=

Yogurt=

Answer 1

Using excel solver

Defining Objective , Z=10B+35M+28C+11P+72F+22Y where B is bread, M is Milk, C is cheese, P is potato, F is Fish, Y is yogurt

Constarints are as follows:

145B +142M=138C+124P+196F+304Y >=1713

4B+11M+7C+1.3P+10F+10.2Y <=52

21B+15.7M+0.4C+39.6P+20Y >=18

2B+7M+13C+0.1P+9F+3Y>=14

F>=1.9

M>=1

B,M,C,P,F,Y>=0

B,M,C,P,F,Y are integers

Putting these constraints in excel solver we get, Total cost as 275 and B=3,M=1,C=0,P=6,F=2,Y=0

Above mentioned constarints were used in excel solver to arrive at result

two constraints which were not visible in above picture