Simplify 30=y=80 , 10=x=30 , p=15x+8y

Problem

p=15*x+8*y, where *10≤x≤30,30≤y≤80

Solution

1. Identify the objective, which is to express the linear function p in terms of its variables x and y given their respective ranges.

2. Analyze the constraints provided for the variables, noting that x is bounded between 10 and 30 and y is bounded between 30 and 80

3. Determine the range of the function p by calculating its minimum and maximum values based on the boundaries of x and y

4. Calculate the minimum value (p_min()) by substituting the lower bounds x=10 and y=30

(p_min())=15*(10)+8*(30)=150+240=390

5. Calculate the maximum value (p_max()) by substituting the upper bounds x=30 and y=80

(p_max())=15*(30)+8*(80)=450+640=1090

Final Answer

390≤p≤1090

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