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Differential and integral calculus p 111-112-113

7-A factory producing electric appliances profits LE.30 in every appliances if it produces 50 appliances monthly. When the production increased than that ,the profit in the appliance decreases by 50 piasters for every extra appliance produced , find the number of appliances produced monthly if the profit is to be maximum .

11- a right triangle is to be constructed using a piece of wire of length 2L.find its dimensions if its area is to be maximum .

12-Awire of length 34cm is divided into two portions. A square is to be constructed from one portion and a circle is to be constructed from the second portion .find the length of each portion if the sum of the two figures is to be minimum.

13-the cost of the fuel consumption of a locomotive is propotional to the square of its speed plus LE100 per hour without regard to its speed .the cost of the fuel consumption is LE 25 per hour when the speed is 25 Km/hour .find its speed if the total cost for one kilometer is to be minimum .

16- the sum of the surface areas of a sphere and a right circular cylinder whose radius is the same as the radius of a sphere equals 25 pia .find the radius of the sphere if the sum of the volumes of the sphere and the cylinder is to be maximum.

17- the point on the curve y2=4x+5 so that the distance between it and the point (3.0)is to be minimum.

18 -a window is formed of a rectangle headed by a semicircle whose diameter

Is coincide with one of the dimensions of the rectangle .if the perimeter of the window equals 6 meters .find the radius length of the semi circle so that the area of the window is to be maximum .

19-if the ability of resistance of a piece of wood with rectangular cross section is directly varying with product of one of the dimensions of the rectangle , amd the square of the other .find the two dimensions of the cross sector of the piece of wood which satisfy maximum ability of resistance given that this piece of wood is taken from a treeof acylindrical shape of diameter 100cm.

20 –in the opposite figure :

Find the area of the rectangle which can be drawn outside the rectangle whose dimensions are the two constants a and b