Quantitative analysis - Assignment Example

Lesson 2 Question Linear programming the optimization alternatives utilizing the graphical solution techniques comes from the vertices, which are the sole viable options to attempt. The similarity is that both the minimization and the maximizations points come from the vertices of the graph. Conversely, the maximization problems in linear programming are found on the graph to depict the total revenue used while the minimization points depict the total cost of operation. Moreover, the vertex possessing the highest profit is the maximization points while the vertex with the lowest points is the minimization pointsQuestion 2 There are five fundamental assumptions and requirements for any linear Programming model that ought to be formulated and utilized.

There is assumption that conditions of certainty occur, which implies that the prevailing numbers within the objective and corresponding constraints are known with the certainty thus not altering during the duration of the study. There is an assumption that proportionality exists within the prevailing objective and constraints. The third assumption entails additivity implying that the sum of entire activities is equivalent to the corresponding sum of the underlying individual activities. The fourth assumption is divisibility that implies that the solutions ought not to be necessarily whole numbers but divisible hence taking any fractional value.

Nevertheless, in case a fraction of the product cannot be achieved the result becomes an integer-programming problem. There is assumption that all the answers and corresponding variables are normally non-negative. Question 3 The statement means that in case a feasible region has either two or more solutions then an infinite number of the solution exists. Moreover, it occurs due to the convexity. Question 4Minimize C = 18x + 22y Subject to: Potassium 5x + 8y ≥ 200 grams Carbohydrates 25x + 6y ≤ 240 grams Protein 4x + 12y ≤ 180 grams x ≥ 0, y ≥ 05x + 8y= 20025x+ 6y=240X=40-8/5y25(40-8/5y) + 6y=240X=4 y= 23C=538Question 5 Maximize P = 100x + 200y Subject to: 3x + y ≥ 6 4x + 5y ≤ 20 2x + 5y ≥ 10 x ≥ 0, y ≥ 0X=1; Y=3P=700Question 6The number of units to produce in order to maximize the profitMaximize P= 120x + 100ySubject to: 6x+4y ≥480 2x+4y ≥240 4y≥200 x ≥ 0, y ≥ 0X=47 Y=50P=10,600Question 7Let number of units of air conditioners be x and number of units of large fan be yMaximize P= 750x+ 1250y Subject to 3x+2y≥240 2x+ y≥140 x ≥ 0, y ≥ 0x=40 ; y=60P=105,000Thus, 40 units of air conditioners and 60 fans would yields the highest profit of 105,000Lesson 3Question 4Maximize 5x + 30ySubject to: 15x + 2y≤ 50 12x + 4y≥ 64 x≥0, y≥0Let x and xbe slack variablesMaximize z: 5x + 30y Subject to: 15x + 2y+ x = 50 12x + 4y + x= 64 x≥0, y≥0Question 5 Maximize 80x + 70y Subject to 2x+ 9x≥ 36 2x+ x≤ 12 2x+ 3x= 24 x ≥ 0, y ≥ 0Let X3 x4 and x5 be slack variables Maximize 80x + 70y Subject to: 2x+ 9x+ X3 = 36 2x+ x + x4 =12 2x+ 3x + x5 = 24Question 6Minimize Z= 10x + 2x Subject to: x+ x≥ 10 3x+ x≤ 12 x≥ 0, y ≥ 0 Let x3 and x4 be slack variables and x5 be the artificial variableSubject to x+ x+ x3 = 10 3x+ x + x4 + x5 = 12 Question 7 Minimize Z= 20x+10x+ 80x Subject to x+ x+ x≥ 6 2x+ 4x+ x= 20 2x+ x≤ 5 x, x, x≥ 0Let x4, x5 and x6 be slack variables and x7 be the artificial variable Minimize Z= 20x+10x+ 80x Subject to x+ x+ x+ x4 = 6 2x+ 4x+ x+ x5 = 20 2x+ x + x6 + x7 = 5Question 8Maximize Z= 26 x1+ 50 x2Subject to 6 x1 + 8 x2 ≤38 6 x1 + 12x2 ≤ 42 x, x≥ 0x1= 5; x2= 1Maximum profit Z= 180Question 9Maximize P = 300x+ 200x+ 100xSubject to: x+ x ≤ 200 x+ x≥ 150 x≤ 50 x≥ 0, x≥ 0, x ≥ 0x= 50x1=100x2=100Maximize P= 55,000Question 10Minimize cost: 50x+ 10x+ 75xSubject to: x- x= 1000 2x+ 2x= 2000 x ≤ 1500 x, x, x ≥ 0Works CitedQuantitative Techniques for Business by Priscilla S.

Altares et al. Quantitative Techniques for Business Management by Praxedes Solina Victoriano. Quantitative Analysis in Management by Richard Levin et al.