Question

1.ABP pizza produces three different items for their customers: pizza, calzone and lahmacun. In order to do so, it uses four different types of ingredients: Cheese, beef, peppers and ham. For a pizza to make, 2 ounce of cheese, 3 ounce of beef, 3 ounce of peppers and 2 ounces of ham are required. For a calzone to make, 2 ounce of cheese, 1 ounce of beef and 4 ounces of ham are required. Finally, for lahmacun to make, 1 ounce of cheese, 4 ounce of beef and 1 ounce of peppers are required. ABP pizza has available 300 ounce of cheese, 200 ounce of beef, 150 ounce of peppers and 250 ounces of ham in total. The pizza sells for $8, the calzone sells for $6, and lahmacun for $7.5.

At the optimal point, how many pizzas should ABP make?

a.38.16

b.22.22

c.48.68

d.0

e.None of the above

2. Now ABP pizza decides to change the price of lahmacun. They have not yet decided on the new price but they want to increase it as much as possible without changing the optimal solution.

What should the new price be for lahmacun?

a.The optimal solution will not change, no matter how much they increase the price of lahmachun.

b.None of the above

c.8

d.They can not increase the price of lahmachun without changing the optimal solution.

e.15

Answer 1

Excel formulation:

Solver inputs:

Solution:

	Pizza	Calzone	Lahmacun
Qty.	48.68	38.16	3.95
Revenue	8	6	7.5	648.03
s.t.
Cheese	2	2	1	177.63	<=	300
Beef	3	1	4	200	<=	200
Peppers	3	0	1	150	<=	150
Ham	2	4	0	250	<=	250

So,

At the optimal point, how many pizzas should ABP make? c) 48.68

Variable Cells
			Final	Reduced	Objective	Allowable	Allowable
	Cell	Name	Value	Cost	Coefficient	Increase	Decrease
	$C$3	Qty. Pizza	48.68421053	0	8	17.5	0.3125
	$D$3	Qty. Calzone	38.15789474	0	6	0.625	4.388888889
	$E$3	Qty. Lahmacun	3.947368421	0	7.5	0.5	5.833333333

As per the sensitivity report, the allowable increase is 0.50. This is the limit up to which the price can be increased without changing the optimal solution.

So,

The new price will be c) 7.5 + 0.5 = 8