Problem Set A (1) The table below shows the calories, fat, and carbohydrates per ounce for three brands of cereal, and the total amount of calories, fat, and carbohydrates required for a special diet....

Problem Set A

(1) The table below shows the calories, fat, and carbohydrates per ounce for three brands of cereal, and the total amount of calories, fat, and carbohydrates required for a special diet.

(i) Using the information in the table above, write a system of three equations.

(ii) Write a system in matrix form
Ax =b.

(iii) Using the Cramer's Rule or Inverse Method, find the amount of each brand of cereal that will give the level of nutrition required.

Extracted text: (2) For the function f(x): –x² – 24x +19 3 (i) Determine the turning points and the values of the function at each turning point. (ii) Determine the point of inflection, any exist. (iii) What is the range of value over which the function is strictly increasing (iv) What is the range of values over which the function is concave upwards. (3) A production manager determines that t months after production on a new product begins, 17t² +13t the number of units produced will be N thousand, where N(t)= (2t +1)² * (i) What would be the level of production 5 months into operations. (ii) What would be the level of production be in the long run.