$(20$ marks$)$ Diet Problem: The "diet problem" concerns with finding a mix of

foods that satisfies requirements on the amount of nutrition. We consider here the

problem of choosing fruits to meet certain nutritional requirements. The nutrition

information of five selected fruits is provided in Table $4$ along with a minimum

required and maximum allowed intake of each type of nutrition in the last two

columns. Your goal is to find the cheapest combination of fruits that will meet

nutritional requirements.

$($a$)$ Formulate a mathematical model for this problem. Solve the problem using

Python and attach your code. Present and interpret the results.

Table $4$: Nutrition and price information per $100$ grams

$($b$)$ Without solving the problem using the software, can you determine how your

optimal solution and optimal spending in $($a$)$ will change if you are also con$-$

cerned with the total fat intake. The fat contained in each of the fruit and

your nutrition requirement on fat is provided in the table below. Verify your

solution by solving the problem numerically.