# Tutor profile: Ahmed E.

## Questions

### Subject: Mechanical Engineering

List five differences between Spark Ignition engines and Compression Ignition engines:

1- SI engines use spark Plugs while CI engines use self-ignition 2- SI engines intake an air-fuel mixture while CI engines intake air only 3- SI engines have combustion occur at about constant volume while CI engines have some combustion occur at constant pressure 4- SI engines use Gasoline fuel while CI engines use Diesel oil fuel 5- SI engines have carburetors or fuel injectors in the intake system while CI engines have fuel injectors in the combustion chamber

### Subject: Industrial Engineering

The question in operations Research: A company produces 2 types of chairs A, B from two raw materials R1 and R2. the basic data is explained as follows: Type A needs 6 tons of R1, and 1 ton of R2 >> it makes a profit of $5000 per ton Type B needs 4 tons of R1 and 2 tons of R2 >> it makes a profit of $4000 per ton The maximum daily available tons of R1 is 24 tons and R2 is 6 tons A market survey indicates that the daily demand for type A chairs cannot exceed that for type B by more than 1 ton. Also a maximum daily demand for type A chairs is 2 tons. the company wants to determine the optimum (best) product mix of both types that maximizes the total daily profit. formulate a Linear programming model for this problem

Step 1: determine the decision variables of the problem: X1= Tons produced daily of type A chairs X2 = Tons produced daily of type B chairs Step 2: Determine your Objective function: Let Z represent the total daily profit (in $ 1000) The objective of the company is to: Maximize Z = 5 * X1 + 4 * X2 Step 3: Identify the constraints of your problem: >> The raw material restrictions: (usage of raw material by both types ) ≤ (maximum raw material availability) >> 6 * X1 + 4 * X2 ≤ 24 and 1 * X1 + 2 * X2 ≤ 6 >> X2 – X1 ≤ 1 ( Market Limit) >> X2 ≤ 2 ( Demand Limit) >> the non-negativity constraints: X1 ≥ 0 & X2 ≥ 0 Step 5: Write your complete Linear Programming Model: Maximize Z = 5 X1 + 4 X2 Subject to: 6* X1 + 4* X2 ≤ 24 (1) X1 + 2 *X2 ≤ 6 (2) – X1 + X2 ≤ 1 (3) X2 ≤ 2 (4) X1, X2 ≥ 0 (5)

### Subject: Calculus

Sketch the region described by the following functions and find its area: Y = X^2 & Y = 2X - X^2

Step one: Draw both functions on the same scale step two: find the points of intersection of the parabolas by solving their equations simultaneously >> X^2 = 2X - X^2 >> 2 (X-1) = 0 >> X = 0 or 1 this will result into 2 points of intersections (0,0) , (1,1) Step three: identify the points on the graph, determine the high and low boundaries of the enclosed area Step four: Total Area: A = integral (from 0 to 1) of { (2X - X^2 - X^2 )dx } >> A = 2 * integral (from 0 to 1) of { (X - X^2 )dx } >> A = 2 * [ (x^2 / 2 ) - (X^3 / 3) } where x from 0 to 1 step five: Subsitute for x = 0 and subtract it from x = 0 >> 2 * (1/2 - 1/3) = 1/3

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