I need help with problem 2 please

Problem 1 is a profit-centered evaluation of the espresso drinks the coffee shop offers: cappuccino, caf latte, espresso, and Americano. Each drink takes a different mix of ingredients to produce: espresso, milk, foam, and water (additional to that used to make the espresso).

Each drink sells for a particular retail price, and the drink components have a specific cost per ounce used.

We will structure our model with daily demand in mind. As we all know, we cannot sell more beverages than customers want to buy (demand), and we cant sell partial beverages either. For cappuccinos, daily demand is 47; for caf lattes, 37; for espresso, 7; and for Americanos, 2.

One thing preventing the coffee shop from setting a production plan that exactly matches those daily demand figures is limited resources, which we will think of as a limited amount of fluid ounces available for the baristas to use. There are 400 oz. of espresso available, 300 oz. of milk, 100 oz. of foam, and 500 oz. of water.

You are charged with creating a model that will help the owner understand what an optimal plan would look like. Specifically, making how many of each drink will maximize profit while meeting all constraints?

Anyone who has been to a coffee shop should recognize that the scenario posed in problem 1 is not very realistic. Rarely, if ever, is service denied because of lack of ingredients budgeted for a particular drink. (If this bothers you, think of this model as a rough first step in figuring out what drinks you might try to attract customers to through your marketing efforts.) Problem 2 addresses a more realistic (and more complex) scenario.

Problem 2. Product Mix with Form Controls

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Problem 2 involves a different scenario, where the caf owner has decided to offer catering packages to local groups. Three catering package types, breakfast, lunch, and coffee break, each consisting of both food and drink options, need to be developed, and their contents will depend on the size of the group. The question is, given the package type and group size, what array of food and drink items will be best for profit? A list of possible menu items (expanded upon from problem 1), along with their costs and retail prices, is found on the Problem 2 worksheet.

Table 1, on the next page, outlines required total items (# of Items) for group sizes from 10 to 50, in intervals of 10. (For now, anyway, we will require group size to be a multiple of 10.) The second column multiplies the number of people by 2, creating the starting assumption that we will provide two items (one drink and one food item) per person. Lastly, the third column, # of Items, adds 5, 7, 9, 11, or 13 (depending on the group size) to the People * 2 value. This (and not merely People * 2) is what we will treat as our conservative estimate of items required, speaking to the fact that some in the group might want seconds, and that running out of items makes both the caterer and the event organizer look bad. So, for example, if the caf will be catering for 10 people, then the bundle should include exactly 25 items (food and drinks combined).

# of People	People * 2	# of Items
10	20	25
20	40	47
30	60	69
40	80	91
50	100	113

Table 1: Number of Items Required

Now, drilling down into the question of what kind of drinks and what kind of food to provide, we need to consider the type of catering. It is more important to provide various coffee drinks at a coffee break than at a lunch event. The table below lists, for each menu item, per-person minimums. For example, at a breakfast event, for every 1 person, we will provide at least .2 cappuccinos, .2 caf lattes, and so on. So if the caf caters to a group of 10 for breakfast, the catering package must contain at least 2 cappuccinos, 2 caf lattes, 2 espressos, and 2 Americanos (10 * .2 for each of those items).

Per-person minimums
	Breakfast	Lunch	Coffee break
Cappuccino (6oz)	0.2	0.1	0.25
Caf latte (10oz)	0.2	0.1	0.25
Espresso (1oz)	0.2	0.1	0.25
Americano (8oz)	0.2	0.1	0.25
Egg and cheese English muffin	0.2	0.1	0
Cookie	0	0.15	0.5
Cinnamon roll	0.2	0.1	0.5
Quiche	0.2	0.6	0

Table 2: Minimums per Item

Constraints

The total items provided, both food and drinks, must equal the conservative estimates (# of Items) found in the first table for the relevant group size.

Separately, the number of food items must be greater than or equal to the number of people expected. The same goes for drinks. This ensures that each person would receive both one drink and one food item, at the very least.

Do not implement an integer constraint with this model, no matter what the results of the Solver run look like.