A large breeder of a particular type of dog wishes

THIS QUESTION IS ABOUT OPTIMIZATION AND SOLVER TABLE
Dog Breeder
A large breeder of a particular type of dog wishes to determine the quantities of available types of dog
food that he should stock so that he can be assured that his dogs meet their nutritional requirements,
but at the least cost possible. He has decided that he can do this by deciding the requirements of each
type of feed for a single dog during one day of operation (he will multiply by the number of days and
number of dogs later). The number of units of each type of basic nutritional ingredient contained
within a kilogram of each feed type is given in the following table, along with the daily nutritional
requirements. The feed costs per kilogram are shown on the bottom row.
Nutritional
Ingredient
Carbohydrates
Protein
Vitamins
Cost ($)

Corn based feed

90
30
10
$4.20

Animal product
based feed
20
80
20
$3.60

Vegetable protein
based fee
40
60
60
$3.00

Minimum Daily
Requirement
200
180
150

a) Define the decision variables (and give them names like x, y, z, etc. using as many variables, and
names, as you need; also provide units for each).
b) Define the constraints using the variables you defined.
c) Using the variables you defined, define the objective function and whether you want to maximize or
minimize it.
d) Implement your model in Excel – what is the optimal solution (please specify the both the value of
your decision variables and your objective function).
Include a readable printout of your model, showing both formulas and row and column headings as
Exhibit 2-A.
e) Suppose there were a vitamin pill available that provides 10 units of vitamin, and costs $.10 per pill.
Without solving the model again, would you consider buying these? Why or why not (base your
argument on the optimal solution only)?
f) A dietary food supplier is offering you protein powder on the cheap and is willing to negotiate the
price. You figure $.5 per unit of protein may be a reasonable price. Augment your model to take this
into account. Would you buy any protein powder at this price point? Include a readable printout of
your augmented model, showing both formulas and row and column headings as Exhibit 2-B

g) Run a SolverTable on the price of unit of protein powder. Identify your walk-away-point (the price
point when you would be indifferent between buying the protein from the food supplier and the
status quo). What is your walk-away price? Include a readable printout of your table as Exhibit 2-C.