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Describe geometrical meaning of indefinite integral. Write down
some properties of indefinite integral.
A company manufacturers and sells x electric drills per month. The monthly cost and price-demand equations are C(x)=74000+70x,
p=220−(x/30) ,0≤x≤5000.
(A) Find the production level that results in the maximum revenue.
(B) Find the price that the company should charge for each drill in order to maximize profit.
(C) Suppose that a 5 dollar per drill tax is imposed. Determine the number of drills that should be produced and sold in order to maximize profit under these new circumstances.
Find a solution u(x,t) to the problem 𝜕𝑢 𝜕𝑡 = 1.71 𝜕^2𝑢/𝜕𝑥^2 , 𝑢(𝑥, 0) = 𝑠𝑖𝑛 ( 𝜋𝑥/2 ) + 3 𝑠𝑖𝑛 ( 5𝜋𝑥/2 ) , 0 < 𝑥 < 2
Evaluate
lim 3nΣr=1 n^2/(4n+r)^3
n→∞
Determine whether the function f (x) = x − x1 is odd, even or neither.
Find the unit normal to the surface 𝑦 = 𝑥 + 𝑧 3 at the point (1,2,1).
A manufacturer knows that if x goods are demanded on a particular week, the total cost and revenue functions will be:𝐶(𝑥) = 14 + 3𝑥 𝑎𝑛𝑑 𝑅(𝑥) = 18𝑥 − 2𝑥 2 respectively.
i. Calculate the level of demand that will maximize profits (6 marks)
ii. Calculate the amount of profit that will be realized at this maximum point. (4 marks)
The quantity demanded per month of a product is 250 units when the unit price is Ksh 1400. The quantity demanded per month of the same product is 1000 when the unit price is Ksh 1100. The quantity suppliers will supply to the market is 750 units when the unit price is Ksh 600 or lower and will supply 2250 units if the price is Ksh 800. Both the Supply and Demand functions are known to be linear. Required
: i. Find the demand function (2 marks)
ii.Find the supply function (2 marks)
iii. find the equilibrium price and quantity (4 marks)
if the total cost of producing x liters of salad oil is C(x)=0.375x^3-0.99x^2-200x+60,000
find the marginal cost at an output of 100litres
A Norman window consists of rectangle surmounted by a semicircle. If the
perimeter of a Norman window is 32 ft, what should be the radius of the
semicircle and the height of the rectangle such that the window will admit most
light?
#340153 on Dec 2023