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a company in the wholesale trade selling sportswear and stocks two brands, a and b, of football kit, each consisting of a shirt, a pair of shorts and a pair of socks. the costs for brand a are sh.50 for a shirt, sh 30 for a pair of shorts and sh10 for a pair of socks and those for brand b are sh.60.25 for a shirt, sh.40 for a pair of shorts and sh.10 for a pair of socks. three customers x, y, z demand the following combinations of brands; x, 36 kits of brand a and 48 kits of brand b y, 24 kits of brand a and 72 kits of brand b z, 60 kits of branda required:i) express the costs of brands a and b in matrix form, then the demands of the customers, x,y and z in matrix form. (5 marks)ii) by forming the product of the two matrices that you obtain in the previous part, deduce the detailed costs to each of the customers. (5 marks)
The weekly sales (RS) at a big store x weeks after the end of an advertising campaign are given
by S(x)= 5000+
5000
X+5 Find the sale for the indicated week's limits
a) S(2),
b) lim S(x)
An office supply company sells Q permanent markers per year at $P per marker. The price-demand equation for these markers is P=10-0.001Q. The total cost of manufacturing Q permanent markers is TC(Q)=5000+2Q.
A. What is the company's maximum profit?B. What should the company charge for the markers, and how many markers should be produce to maximize the profit?
Find the inverse Laplace transforms of the following functions:
(a)
s + 3 /(s^2 + 6s + 13)
(b)
2s + 3/(s^2+6s+13)
The weekly sales (RS) at a big store x weeks after the end of an advertising campaign are given
by S(x)= 5000+
5000
X+5 Find the sale for the indicated week's limits
a) S(2),
b) lim S(x)
1) Find the following limit: lim (x→0) ln(1 + (sin(2x))^2 )/ (1 − cos2(x)).
2) Determine type of the differential equation y`` − 2y` + y = sin x:
◦ partial differential equation.
◦ first order differential equation.
◦ linear differential equation with constant coefficients.
◦ linear nonhomogeneous differential equation.
◦ nonlinear homogeneous differential equation.
3) Write general solution of the differential equation x^(2) y'' + xy' + a^(2) y = 0:
◦ Ax^2 + Bx
◦ Ax^a + Bx^−a
◦ Ax^ia + Bx^−ia
◦ Ae^ax + Be^−ax
◦ Ae^iax + Be^−iax
◦ explicit algebraic form does not exist.
Find the general solution given y1=x2 is a particular solution of x^2y"-3xy'+4y=0.
f(x,y)=(x^3y^3)/(x^3+y^3) at (x,y)=(0,0)
f(x,y)=y/√(x^2+y^2). at (x,y)=(0,0)
