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An Italian restaurant offers a choice of pasta or pizza meals. It costs $3 to make a pasta dish, which it sells for $13. The corresponding figures for pizzas are $2 and $10, respectively. The maximum number of meals that can be cooked in a week is 1200 and the restaurant has a weekly cost budget of $3000. How many pasta and pizza dishes should be cooked each week to maximize profit?

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Answer:

Number of pasta dishes = 600
Number of pizza dishes = 600

Step-by-step explanation:

Let x represent the number of pasta meals cooked

Let y represent the number of pizza meals cooked

Since total number meals that can be cooked in one week is 1200 we get the equation

x + y = 1200     [1]

Each pasta meal costs $3 to make so x pasta meals will cost $3x

Each pizza meal meal costs $2 to make so y pizza meals will cost $2y

Total cost in $ = 3x + 2y

Since the weekly cost budget = 3000
3x + 2y = 3000   [2]

We have two equations [1] and [2] to solve in two unknowns, x and y. To solve we can proceed as follows;

Multiply [1] by 2 to make the coefficients of y the same:
2x + 2y = 2400 [3]

Subtract [3] from [2] to eliminate y

3x + 2y = 3000
                         -
2x + 2y = 2400
---------------------
x            = 600
----------------------

Substitute 600 for x in equation [1]
x + y = 1200 becomes
600 + y = 1200

y = 1200 - 600
y = 600

So the maximum number of pasta meals = 600 and
maximum number of pizza meals = 600