## 1. Solve the following LP model by Simplex Method and find x1, x2 and x3.

Question 1. Solve the following LP model by Simplex Method and find x1, x2 and x3. Max Z= 4×1 2×2 2×3 s.to3x1 6×2 – 3×3 ≤ 903×1 x2 x3 ≤ 180×1- x2 x3 ≤ 60×1, x2, x3 ≥ 02. acreate a problem and define the decision variables to meet the following LP formulation. A LP model is constructed for you, you will just write down a problem according to this LP formulation. Max Z= 2×1 3×2 5×3 s.tox1 x2 x3 ≥ 302×1 3×2 4×3 ≤ 100×1 – 2×2 ≤ 0x1- x3 ≤ 50×1, x2, x3 ≥ 0

## For each of the following relations: – State whether it is a function. Justify your reasoning.

Question For each of the following relations: – State whether it is a function. Justify your reasoning. – State the domain and range.Question 1 {(1, 9), (2, 7), (3, 5), (4, 3)} Question 2Question 3 Question 4f(x)=2√x-3 5Use the functions f(x)=x^2-2x 4 and g(x)=3÷2(x-1), to determine:**Leave answers in rational form**Question 5f(-1)Question 6f(0)Question 7g(1÷2)Question 8g(1)Determine the inverse, algebraically, of each of the following.Question 9f(x)=1÷2(x-4)^2 1Question 10f(x)=2x-5÷7For each of the parent functions, below, describe transformations made and state the domain and range for the function, g(x).Question 11f(x)=x^2 ,g(x)=-2f(x-2)Question 12f(x)=√x ,g(x)=f(-2x) 1Question 13f(x)=1÷x ,g(x)=3f(-x) 1Question 14The point (1,6) is on the graph of y=f(x). What would the new co-ordinates be for the function g(x)=2f(1÷3(x-1)) 5 ?

## A microchip company plan to extend their business by adding some of

Question A microchip company plan to extend their business by adding some of SMT machines. Based on Production Planning Control (PPC) Department information, the scheme to buy the machine as in Table 1.Table 1: The Cost Scheme of SMT Machine Budget Quantity Cost (in 0000 RM) 1 3 5 14 20 55.25a) Draw a graph for the cost scheme of SMT machines.(7 marks)b) Generate the mathematics equation for the cost scheme for SMT Machine (10 marks)c) Calculate the cost for SMT Machine if the company want to buy 18 units.

## 1. Explain what the term inverse means with respect to a quadratic

Question 1. Explain what the term inverse means with respect to a quadratic function. How are the domain and range of a quadratic function related to the domain and range of its inverse?2. Your friend attempted to graph the equationf(x)=-2(x-3)^2 1 . Based on their graph of the parent function (solid), and the transformed function (dashed) below, describe which transformations have been applied correctly, and which have not. Justify your answer.

## Let R be the ring Z5 ⊕ Z5

(a) Let S1 = {(r, r): r ∈ Z5}. Is S1

Question Let R be the ring Z5 ⊕ Z5

(a) Let S1 = {(r, r): r ∈ Z5}. Is S1 (with the operation ) a subgroup of R? Is S1 a subring of R? (b) Let S2 = {(r, −r): r ∈ Z5}? Is S1(with the operation ) a subgroup of R? Is S2 a subring of R?

## Complete the table, for the following investments, which shows the

Question Complete the table, for the following investments, which shows the performance (interest and balance) over a 5-year period.Suzanne deposits $40004000 in an account that earns simple interest at an annual rate of 4.54.5%. Derek deposits $40004000 in an account that earns compound interest at an annual rate of 4.54.5% and is compounded annually.YearSuzanne’s Annual InterestSuzanne’s BalanceDerek’s Annual InterestDerek’s Balance11$____$____$____$____22$____$____$____$____33$____$____$____$____44$____$____$____$____55$____$____$____$____Complete the following table.(Round to the nearest dollar as needed.)YearSuzanne’s Annual InterestSuzanne’s BalanceDerek’s Annual InterestDerek’s Balance11$nothing$nothing$nothing$nothing

## Here’s an example of a real-world optimization problem.

Your friend has a fabulous recipe for salsa, and he wants to

Question Here’s an example of a real-world optimization problem.

Your friend has a fabulous recipe for salsa, and he wants to start packing it up and selling it. He can rent the back room of a local restaurant any time he wants, complete with their equipment, for $100 per time. It costs him $2 a jar for the materials (ingredients for the salsa, jars, labels, cartons) and labor (you and a couple of friends of his) for each jar he makes. He can sell 12,000 jars of salsa each year (I told you it was a fabulous recipe!), with a constant demand (that is, it’s not seasonal; it doesn’t vary from week to week or month to month). It costs him $1 a year per jar to store the salsa in the warehouse he ships from. He wants to find the number of jars he should produce in each run in order to minimize his production and storage costs, assuming he’ll produce 12,000 jars of salsa each year. Post your suggestions on how would you help him figure this out.