Question

The owner of an ice cream shop is experiencing declining sales. The owner wants to make an ice cream sundae that is loaded with everything on the menu as long as it meets the requirements. Money is no object. The ingredients are listed below:

Item	Sodium	Sugar	Calories	Cost
Ice Cream	50	17	220	0.25
Cone	330	9	260	0.15
Whipped Cream	310	6	7	0.1
Cherries	1	2	10	0.09
Syrup	260	0	5	0.03
Sprinkles	3	0	4	0.04
Walnuts	160	0	20	0.02
Chocolate Chips	3	0	9	0.04

You must include at least one of every item but cannot put more than 6 of each item

You must use whole its (for example, no half servings of walnuts)

The final sundae must contain no more than 3000 sodium, no more than 150 sugar, and no more than 3000 calories

For quality purposes, you must keep the amount of syrup and chocolate chips the same

You also must keep the amount of walnuts and sprinkles the same.

You must use exactly two cones.

What is the most expensive sundae you can make that meets these requirements?

Answer 1

Below excel screenshot show the approach for solving this problem using linear programming.

The most expensive sundae will include following:

Item	Quantity
Ice Cream	6
Cone	2
Whipped Cream	3
Cherries	6
Syrup	1
Sprinkles	5
Walnuts	5
Chocolate Chips	1

Total cost of $3.01

If you liked my answer, please give thumbs up/ likes. Thank you!