Question

An animal feed to be mixed from soybean meal and oats must contain at least120 lb of​ protein, 27 lb of​ fat, and 10 lb of mineral ash. Each sack of soybeans costs $15 and contains 50 lb of​ protein, 9 lb of​ fat, and 55 lb of mineral ash. Each sack of oats costs ​$5 and contains 15 lb of​ protein, 5 lb of​ fat, and 1 lb of mineral ash. How many sacks of each should be used to satisfy the minimum requirements at minimum​ cost?

Answer 1

Solution Image (with instructions) below and the table sheet for reference below that.

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Requirements Decision Objective function: MINIMIZE total cost Vanables Total cost of soyabean and oats sacks (Should be minimized) Use add-in Solver; green cell: objective function; minimize Yellow cells are decision variables; Constraints are as below 40 <-- protein fat mineral ash 120 27 10 soyabearn oats Constraints Products 120 - Total proteins should be atleast as much as required Total fats should be atleast as much as required Total mineral ashes should be atleast as much as required 130 mineral ash proteinfat 15 28 >= 112 27 < 10 cost soyabearn 50 15 9 <Total sacks of soyabeans should be an integer <Total sacks of oats should be an integer oats integer integer IS 2 is

Requirements

Decision variables

Objective function: MINIMIZE total cost

40

<--

Total cost of soyabean and oats sacks (Should be minimized)

protein

120

soyabean

2

Use add-in Solver; green cell: objective function; minimize Yellow cells are decision variables; Constraints are as below

fat

27

oats

2

mineral ash

10

Constraints

Products

130

>=

120

<--

Total proteins should be atleast as much as required

cost

protein

fat

mineral ash

28

>=

27

<--

Total fats should be atleast as much as required

soyabean

15

50

9

55

112

>=

10

<--

Total mineral ashes should be atleast as much as required

oats

5

15

5

1

2

is

integer

<--

Total sacks of soyabeans should be an integer

2

is

integer

<--

Total sacks of oats should be an integer