Question: Calculating Objective function co-efficients:

The objective is to Maximize total profit. Profit is calculated for each variable by subtracting cost from the selling price.

 For Pizza slice, Cost/slice=$6/8=$0.75

 Total space available=3*4*16=192 sq feet =192*12*12=27,648 in- square

The oven will be refilled during half time.

Thus, the total space available=2*27,648= 55,296 in-square

 Space required for a pizza=14*14=196 in-square

Space required for a slice of pizza=196/8=24 in-square approximately.

Thus, Objective function for the model can be written as:

Maximize Total profit Z = $0.75 X 1 + 1.05 X 2 +1.35 X 3

Subject to constraints:

$0.75 X 1 + .0.45 X 2 + 0.90 X 3 <= 1,500 (Budget constraint)

24 X 1 + 16 X 2 +25 X 3 <= 55,296 (Inch square Of Oven Space )

X 1>=X2 + X 3 (at least as many slices of pizza as hot dogs and barbeque sandwiches combined)

X2/X3>= 2.0 (at least twice as many hot dogs as barbeque sandwiches)

This constraint can be rewritten as:

X2-2X3>=0

X 1, X 2, X 3 >= 0

Final Model:

Maximize Total profit Z = $0.75 X 1 + 1.05 X 2 +1.35 X 3

Subject to:

$0.75 X 1 + .0.45 X 2 + 0.90 X 3 <= 1,500 (Budget)

24 X 1 + 16 X 2 +25 X 3 <= 55,296 (In-square Of Oven Space)

X 1-X2 - X 3>=0 (at least as many slices of pizza as hot dogs and barbeque sandwiches combined)

X2-2X3>=0 (at least twice as many hot dogs as barbeque sandwiches)

X 1, X 2, X 3 >= 0 (Non negativity constraint)

Price: $2.99

Solution: The downloadable solution consists of 5 pages
Deliverable: Word Document