Final answer:
Hassan is baking cookies for his school bake sale fundraiser, Hassan should make 400 oatmeal chocolate chip cookies and 200 peanut butter cookies in order to maximize his profit.
Step-by-step explanation:
To solve this optimization problem, let's define the number of oatmeal chocolate chip cookies as 'm' and the number of peanut butter cookies as 'p'.
Given that Hassan wants to maximize his profit, we can express his objective function as:
Profit = 0.25m + 0.20p
Now, let's consider the constraints:
Total number of cookies: m + p ≤ 700
Maximum number of peanut butter cookies: p ≤ 400
Minimum number of peanut butter cookies: p ≥ 0.5m
To find the optimal values for 'm' and 'p', we can solve this linear programming problem using a graphing method or a solver tool like the Simplex method.
The optimal values will be the ones that maximize the profit while satisfying all the constraints.
However, we can make some observations to simplify the problem:
To maximize profit, we would want to make the maximum number of oatmeal chocolate chip cookies (m = 400).
Since we need to make at least half as many peanut butter cookies as oatmeal chocolate chip cookies, the minimum number of peanut butter cookies would be p = 0.5 * 400 = 200.
Therefore, the optimal values for 'm' and 'p' are m = 400 and p = 200. By making 400 oatmeal chocolate chip cookies and 200 peanut butter cookies, Hassan will be able to maximize his profit.