Question 887173
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the feasible region is above the line of y = 10 and below the line of y = 30 and to the right of the line x = 30 and to the left of the line x = 80 and below the line of y = 80 - x
the boundary points of the feasible region are (30,30) and (30,10) and (50,30) and (70,10).
your maximum profit will be at one of these boundary points.
your profit equation is p = 25*x + 55*y
x = number of bookshelves
y = number of desks
when x = 30 and y = 30, profit is 30*25 + 30*55 = 2400
when x = 30 and y = 10, profit is 30*25 + 10*55 = 1300
when x = 50 and y = 30, profit is 50*25 + 30*55 = 2900 *****
when x = 70 and y = 10, profit is 70*25 + 10*55 = 2300
maximum profit is when you make 50 bookshelves and 30 desks.
the line y = 80-x is derive from the equation x + y <= 80 which is the maximum of bookshelves or desks that can be made.
the feasible region satisfies all the constraints.
number of bookshelves and desks can't be greater than 80 (y <= 80-x).
number of bookshelves has to be greater than or equal to 30 and less than or equal to 80 (x >= 30, x <= 80).
the number of desks has to be greater than or equal to 10 and less than or equal to 30 (y>= 10, y <= 30).