FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 3.55- A firm produces x units of output per week ata a total cost of ` 3 2
(^1) x x 5x 3.
3
(^) − + +
Find the output
levels at which the marginal cost and the average cost attains their respective minima.[Ans. 1, 3/2]
- A radio manufacture finds that he can sell x radios per week ar Rs. p each, where
p 2 100 .x
4
−^ −^
(^)
His cost of productiono of x radios per week is Rs.
x^2
(^) 120x+ 2.
show that his profit is maximum when the production is 40 radios per week. Find also his maximum
profit per week. [Ans. ` 1600]
- The total cost function of a firm is c x 3x 10x 10.^1 x^3 −^2 + + Where c is the rotal cost and x is output.
A tax at the rate of Rs. 2 per unit of output is imposed and the producer adds it to his ost. If the market
demand function is given by p = 2512 – 3x, where p is the price per unit of output, find the profit
maximumsing output and hence the price. [Ans. 50 ; rs. 2362]- Find two positive numbers whose product is 16 having minimum sum [Ans. 4,4]
- The sum of two numbers is 18. Find the maximum value of their product. [Ans. 81]
- Find two positive numbers whose sum is 15 and the sum of whose square is minimum. [Ans. 15 152 2, ]
- Of all the rectangles, each of which has perimeter 40cm., find the one having maximum area.
[Ans. Square of side 10cm ; 100 sq. cm.] - A farmer can afford to buy 800 metres of wire fencing. He wishes to enclose a rectangular field of
largest possible area. What should the dimensions of the field be? [Ans. 200m; 200m]
OBJECTIVE QUESTION- If y = (2 – x)^2 find dydx [Ans. x – 4]
- If y = x^3 find
dy^2
(^) dx^ +^1 , when x = 1 [Ans. 10]
- Differentiate x^6 w.r.t.x^2 [Ans. 3x^4 ]
- If y = log (4x) find dydx[Ans.^1 x]
- If y x 1=( +)^2 find dydx [Ans.
1 1
x+ ]
- If
y x^1
x
= + find find 2x ydy
dx+ [Ans. 2 x] - If y = logx find
2
d ydx 2 [Ans. 2
1
−x ]