Short Answer TypeManufacturer can sell x items at a price of rupees 
The cost price of x items is Rs. 
Find the number of items he should sell to earn maximum profit.
A firm has found from experience that its profit as a function of x, the amount produced, is given by
Find the value of x that maximises the profit.
A beam of length l is supported at one end. If W is the uniform load per unit length, the bending moment M at a distance x from the end is given by 
maximum value. Find the point on the beam at which the bending moment has th
Long Answer TypeA wire of length 36 cm is cut into two pieces. One of the pieces is turned in the form of a square and the other in the form of an equilateral triangle. Find the length of each piece so that the sum of the areas of the two be minimum.
Total length of wire = 36 cm
Let x cm be length of each side of square and y cm be length of each side of quilateral triangle.
Length of wire used for square = 4x cms
and length of wire used for triangle = 3y cms
∴ 4x + 3y = 36 ⇒ 3y = 36 – 4x
...(1)
Let A denote the sum of the areas of square and equilateral triangle.
Length of piece required for square = 4x = 
and length of piece required for triangle = 3y = 36 - 4x
A window consists of a semi-circle with a rectangle on its diameter. If the perimeter of the window is 30 metres, find the dimensions of the window in order that its area may be maximum.
Or
A window is in the form of a rectangle surmounted by a semi-circle. If the total perimeter of the window is 30 m. find the dimensions of the window so that maximum light is admitted.
A wire of length 28 m is to be cut into two pieces. One of the pieces is to be made into a square and the other into a circle. What should be the length of the two pieces so that the combined area of the square and the circle is minimum?
Short Answer Type
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