Al Forno is a local pizza restaurant that is participating in an
upcoming Italian Heritage festival this Saturday. At the festival
Al Forno will have a small tent and be selling slices of pizza to
festival attendees. On this occasion Al Forno’s owners know that
any kind of pizza offered will sell. Al Forno will offer plain,
meat, vegetable, and supreme pizzas for sale by the slice at the
festival. Each variety has its own requirement for sauce, cheese,
dough, and topings as shown in the table below. Each variety has
its own selling price per slice. Al Forno wishes to maximize
revenues from sales of slices of pizza.
|
Cheese |
Meat |
Vegetable |
Supreme |
Available |
|
|
Dough (oz.) |
5 |
5 |
5 |
5 |
125 lbs. |
|
Sauce (oz.) |
3 |
3 |
3 |
3 |
7 gallons |
|
Cheese (oz.) |
4 |
3 |
3 |
4 |
100 lbs. |
|
Meat (oz.) |
0 |
3 |
0 |
2 |
50 lbs. |
|
Vegetables (oz.) |
0 |
– |
3 |
2 |
30 lbs. |
|
Price/Slice |
$5 |
$8 |
$6 |
$9 |
a) Formulate and solve the linear programming model which will
determine the mix of pizza types to maximize revenue. Make sure
your model allows for the number of slices produced of each type to
be at least 15% of the total number of slices produced.
b) Al Forno employee Buster Bocelli can be ready at main
restaurant to bring more of any ingredients required to make more
pizza slices and increase revenue. He’ll deliver them to the
festival quickly in the restaurant’s delivery vehicle, the
Fornomobile. According to your model which ingredient(s) would be
immediately required to increase units and revenue?
