Question

Problem 1

A farm has been experimenting with a special diet for its horses. The feed components for the diet are

a standard feed product, a vitamin-enriched oat product, and a new vitamin and mineral feed additive

(detail below). The minimum daily diet requirements for each horse are 3 units of ingredient A, 6 units

of ingredient B, and 4 units of ingredient C. In addition, to control the weight of the horses, the total

daily feed for a horse should not exceed 6 pounds. The farm would like to determine the minimum-

cost mix that will satisfy the daily diet requirements.

Ingredients [in units] to Produce One Pound of Special Die

Feed Component	Standard	Enriched Oat	Additive
Ingredient A	0.8	0.2	0.0
Ingredient B	1.0	1.5	3.0
Ingredient C	0.1	0.6	2.0
Cost Per Pound	$0.25	$0.50	$3.00

On a separate piece of paper, define the variables and formulate the mathematical model for this problem.

Enter the model into Excel's Solver and solve it. How many pounds of Standard product, Enriched Oat, and Additive should be used in the mix to generate the lowest possible total cost?

Please complete on excel using solver so I can see how to format and what cells to link

Answer 1

Let X,Y,Z pounds be the quantities of Standard, Enriched Oat, and Additive feed respectively used in the daily feed mix of a horse.

We want to find these quantities and hence these are decision variables.

The total cost of X,Y,Z pounds of these components is

The farm would like to minimize this cost. Hence this is the objective function

Finally the constraints.

The minimum daily diet requirements for each horse are 3 units of ingredient A

The total amount of ingredient A from X,Y,Z pounds is 0.8X+0.2Y+0*Z. This needs to be at least 3

The minimum daily diet requirements for each horse are 6 units of ingredient B

The total amount of ingredient B from X,Y,Z pounds is 1X+1.5Y+3Z. This needs to be at least 6

The minimum daily diet requirements for each horse are 4 units of ingredient C

The total amount of ingredient C from X,Y,Z pounds is 0.1X+0.6Y+2Z. This needs to be at least 4

In addition, to control the weight of the horses, the total daily feed for a horse should not exceed 6 pounds.

The LP model is

Minimize

s.t.

Prepare the following sheet

to get this

set up the solver using data--->solver

get this

ans: 3.51 pounds of Standard product, 0.95 pounds of Enriched Oat, and 1.54 pounds of Additive should be used in the mix to generate the lowest possible total cost while meeting the daily dietary requirement of a horse.