Pasta without sauce is a naked pasta
- Author:
- Simona Riva
You have then created a new pasta shape, and had great success selling it to a catering company.
But the catering company still needs your help as advisor for their financial planning.
One of the best sauces for this shape of pasta is pesto, which is made with olive oil, basil, pine nuts, grated Parmesan cheese, and garlic.
The doses of each ingredient depend on the weight of basil.
Consider the following table that shows the ingredients, doses, and the wholesale price of each ingredient.
Sauce for one serving
To make enough pesto for 6 people, we need 150g of basil. How much does a portion (for 1 person) of pesto cost? (Enter the exact answer)
The catering company is now evaluating whether producing their own pesto, or buying it ready made from a food company, that sells pesto at €1/portion, with a 2.1% reduction of this price every 10 portions bought.
The catering company is planning to need 150 portions each day.
Write the expression of the function that models the price of pesto purchased at the food company. The variable n indicates the number of sets of 10 portions of pesto.
Write the expression of the function that models the price of pesto, when made by the catering company.
Which option is the cheapest for the catering company?
A graph speaks more than a thousand words.
Draw the graphs of the two functions, and , and deduce from the graph which option is the cheapest for 150 portions.
Confirm your conjecture numerically
Which equation do you need to solve to know when the price of pesto made by the catering company is the same as the purchased one?
Solve the equation and write the result, rounded to 2 decimal places. Discuss the result for a production or purchase of 150 portions.