python

appetizer = [[10,7], [11,9], [13,10], [9,6], [3,4]] #where 1st value is rating, and second is cost of appetizer.
main = [[13, 20], [23, 25], [14,21], [8, 15], [12,18]] #where 1st value is rating, and second is cost of main course.
dessert = [[5,3], [6,4], [8,5], [9,7], [11,8]] #where 1st value is rating, and second is cost of desserts.
all = []
for i in appetizer:
    for m in main:
         for n in dessert:
              if i[1] + m[1] + n[1] <=32: # we cannot spend more than 32$.
                  all.append(i[0] + m[0] + n[0]) #total alternate yumminess.

print max(all)

that prints the answer $\boxed{32}$

This is a form of the knapsack problem; because there were only a few items, I decided just to bash it:

(How do you enter source code? Mine gets really messed up at any for loop)

It's cool to see these problems that are examples of real problems in computer science (knapsack, traveling salesman, ...)

I'm a DBA, so I used SQL to solve this problem ;) If you're not familiar with SQL, I'd advise you to be. It's a really good language and useful for a lot of things...

First, I created three tables, to store the data of Main Courses, Appetizers and Deserts: CREATE TABLE appetizers (name VARCHAR2(30), price NUMBER, yumminess NUMBER); CREATE TABLE main_courses (name VARCHAR2(30), price NUMBER, yumminess NUMBER); CREATE TABLE deserts (name VARCHAR2(30), price NUMBER, yumminess NUMBER);

Then, I inserted the values on each table: --Appetizers: INSERT INTO appetizers VALUES ('Nachos', 7, 10); INSERT INTO appetizers VALUES ('Taquitos', 9, 11); INSERT INTO appetizers VALUES ('Sampler', 10, 13); INSERT INTO appetizers VALUES ('Quesadilla', 6, 9); INSERT INTO appetizers VALUES ('Chips and Salsa', 4, 3);

--Main Courses INSERT INTO main courses VALUES ('Chimichanga', 20, 13); INSERT INTO main courses VALUES ('Steak Fajitas', 25, 23); INSERT INTO main courses VALUES ('Chicken Fajitas', 21, 14); INSERT INTO main courses VALUES ('Beans and Rice', 15, 8); INSERT INTO main_courses VALUES ('Fish Tacos', 18, 12);

--Deserts INSERT INTO deserts VALUES ('Ice Cream', 3, 5); INSERT INTO deserts VALUES ('Milkshake', 4, 6); INSERT INTO deserts VALUES ('Fried Ice Cream', 5, 8); INSERT INTO deserts VALUES ('Chocolate Cake', 7, 9); INSERT INTO deserts VALUES ('Cheescake', 8, 11);

(Don't forget to Commit) COMMIT;

Then, using this SQL query: SELECT * FROM ( SELECT a.name||', '||b.name||', '||c.name foods, a.price + b.price + c.price price, a.yumminess + b.yumminess + c.yumminess yumminess FROM appetizers a, main_courses b, deserts c WHERE a.price + b.price + c.price <= 32 ORDER BY 3 DESC, 2 DESC ) WHERE rownum = 1;

I was able to determine all the sums of all possible combinations of each food, filter only those with price less then or equal to 32, order them decreasingly based on yumminess and price (respectively) and finally just select the first row!

Simple as that ;)

Keep in mind that this setup seems complicated, but is really simple. And it works perfectly for much bigger datasets...

//Here is a solution in C# //

        ArrayList ar = new ArrayList();
        double sm = 0;
        Hashtable ht1 = new Hashtable();
        Hashtable ht2 = new Hashtable();
        Hashtable ht3 = new Hashtable();

        int[] appetizer = { 7, 9, 10, 6, 4 };

        ht1["7"] = 10;
        ht1["9"] = 11;
        ht1["10"] = 13;
        ht1["6"] = 9;
        ht1["4"] = 3;

        int[] maincourse = { 20, 25, 21, 15, 18 };

        ht2["20"] = 13;
        ht2["25"] = 23;
        ht2["21"] = 14;
        ht2["15"] = 8;
        ht2["18"] = 12;

        int[] desert = { 3, 4, 5, 7, 8 };

        ht3["3"] = 5;
        ht3["4"] = 6;
        ht3["5"] = 8;
        ht3["7"] = 9;
        ht3["8"] = 11;


        for (int i = 0; i < 5; i++)
        {
            for (int j = 0; j < 5; j++)
            {
                for (int k = 0; k < 5; k++)
                {

                    sm = appetizer[i] + maincourse[j] + desert[k];

                    if (sm > 32)
                    {
                        continue;
                    }
                    else
                    {
                        int aa = int.Parse(ht1[appetizer[i].ToString()].ToString()) + int.Parse(ht2[maincourse[j].ToString()].ToString()) + int.Parse(ht3[desert[k].ToString()].ToString());

                        if (aa == 32)
                        {
                            ar.Add(aa);
                        }

                    }
                }
            }
        }


        MessageBox.Show(FindMax(ar).ToString());

i = [7,9,10,6,4,10,11,13,9,3]

j = [20,25,21,15,18,13,23,14,8,12]

k = [3,4,5,7,8,5,6,8,9,11]

x = y = z = 0

while x < 5:

y = 0 

while y < 5:

    z = 0

    while z < 5:

        A = i[x] + j[y] + k[z]

        if A <= 32:

            print("yumminess" = i[x+5]+j[y+5]+k[z+5])

        z = z + 1

    y = y + 1

x = x + 1

Python Solution:

class food(object):
    def __init__(self, name, price, yumminess):
        self.name = name
        self.price = price
        self.yumminess = yumminess

appetizers = [food('Nachos', 7, 10),
              food('Taquitos', 9, 11),
              food('Sampler', 10, 13),
              food('Quesadilla', 6, 9),
              food('Chips and Salsa', 4, 3)]

main_courses = [food('Chimichanga', 20, 13),
               food('Steak Fajitas', 25, 23),
               food('Chicken Fajitas', 21, 14),
               food('Beans and Rice', 15, 8),
               food('Fish Tacos', 18, 12)]

deserts = [food('Ice Cream', 3, 5),
          food('Milkshake', 4, 6),
          food('Fried Ice Cream', 5, 8),
          food('Chocolate Cake', 7, 9),
          food('Cheescake', 8, 11)]

bestYumminess = 0

for appetizer in appetizers:
    for main_course in main_courses:
        for desert in deserts:
            if appetizer.price + main_course.price + desert.price <= 32:
                totalYumminess =  appetizer.yumminess + main_course.yumminess + desert.yumminess               
                if bestYumminess < totalYumminess:
                    bestYumminess = totalYumminess

print bestYumminess                    

>>> 32

Assign each selection an index that equals (yumminess score - price). For example, the steak fajitas have an index of -1 because 24 - $25 = -1. The total yumminess score (if Danny spends $32) is equal to 32 plus the sum of all of the (yumminess score - price) indexes for each selection that Danny picks. The main courses are the most expensive, so we choose one of them and then try to maximize the sum of the (yumminess score - price) indexes for Danny's dessert and appetizer choices while spending $32.

For example, if Danny orders the $20 chimichangas, he has $12 left to spend on appetizer and dessert. The appetizers with the highest (yumminess score - price) index are the $7 nachos, the $10 sampler, and the $6 quesadilla, which all have an index of +3. Similarly, the desserts with the highest (yumminess score - price) index are the $5 fried ice cream and the $8 cheesecake, which are tied at an index of +3. Ideally, we'd like to spend exactly $12 on the dessert and appetizer while choosing from those with the highest index to maximize the yumminess score. We can achieve this by buying the $7 nachos and the $5 fried ice cream, which have a combined index of +6. The chimichangas have an index of -7, so the maximum yumminess score for an order with chimichangas is 32 + 6 - 7 = 31.

Similarly, we can show that the maximum yumminess scores for orders with the steak fajitas, the chicken fajitas, the beans and rice, and the fish tacos are 31, 31, 30, and 32, respectively. Therefore, the maximum yumminess score is 32 , achieved by ordering the fish tacos with the quesadilla to start and a cheesecake for dessert. Yummy!

here is piece of code which finds the best option

App = ([10, 7],[11, 9],[13, 10],[9,6], [3,4])

mc = ([13,20],[23,25],[14,21],[8,15],[12,18])

de = ([5,3],[6,4],[8,5],[9,7],[11,8])

totVal = 0 totYummy = 0 for i in range(0,5): a = App[i] for j in range(0,5): m = mc[j] for k in range(0,5): d = de[k] totYum = a[0]+m[0]+d[0] totVal = a[1]+m[1]+d[1] if totVal <=32 and totYummy < totYum: totYummy = totYum print 'App = ', i, 'mc = ', j, 'de = ', k,'totYum = ', totYum, 'totVal = ', totVal