I need help solving this. I only need to write the constraint equation and objective function (don't have to find the minimum cost) using variables x and y. The question states that I'm framing a door that's in the shape of a rectangle with a semicircle on top (no framing along the dotted line). I plan to use 20 ft of framing and the cost of framing for the straight edges is $2/ft and for the circular edge $5/ft. The rectangle has width of "x" and height of "y". Obviously the objective is to minimize cost and the constraint is that there's only 20ft of framing, but I don't know how to use the variables to create a function/equation for the constraint and objective. Especially since there's a semicircle on top, which I know the equation for the perimeter of a semicircle is pi*r+d, but in this case, I think I wouldn't account for "d" because the framing along the dotted line is said to be not part of the question. I'm just not sure how to incorporate the semicircle into the equation.
I need help solving this. I only need to write the constraint equation and objective function (don't have to find the minimum cost) using variables x and y. The question states that I'm framing a door that's in the shape of a rectangle with a semicircle on top (no framing along the dotted line). I plan to use 20 ft of framing and the cost of framing for the straight edges is $2/ft and for the circular edge $5/ft. The rectangle has width of "x" and height of "y". Obviously the objective is to minimize cost and the constraint is that there's only 20ft of framing, but I don't know how to use the variables to create a function/equation for the constraint and objective. Especially since there's a semicircle on top, which I know the equation for the perimeter of a semicircle is pi*r+d, but in this case, I think I wouldn't account for "d" because the framing along the dotted line is said to be not part of the question. I'm just not sure how to incorporate the semicircle into the equation.
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