Operations Research Answers

The table mentioned below shows the “Gross Production of Energy by Two Sources in India from 2010-11 to 2015-16”. Adopt Exponential Smoothing Method. Consider the Alpha (α) values 0.2, 0.5, 0.7 and find out the one that is comparatively good for the prediction Forecast the value for year 2016-17. Year Coal - (Million Tones) Lignite - (Million Tones) 2010-11 532.7 37.73 2011-12 539.95 42.33 2012-13 556.4 46.45 2013-14 565.77 44.27 2014-15 609.18 48.27 2015-16 639.23 43.84 Source: Open Government Data (OGD) Platform India

A bed mart company is in the business of manufacturing beds and

Pillows. The company has 40 hours for assembly and 32 hours for

finishing work per day. Manufacturing of a bed requires 4 hours for

Assembly and 2 hours for finishing. Similarly a pillow requires 2 hours

for assembly and 4 hours for finishing. Profitability analysis indicates

that every bed would contribute Birr 80, while a pillow contribution is

Birr 55 respectively. Maximise 1170x1 + 1110x2

Subject to: 9x1 + 5x2 ≥ 500

-Find graphically the feasible region and the optimal solution

An organization is interested in the analysis of two products that can be produced from the idle time of labour, machine and investment. It was notified on the investigation that the labour requirement of the first and the second products was 4 and 5 units respectively and the total available man-hours were 48. Only the first product required machine hour utilization of one hour per unit and at present only 10 spare machine hours are available. The second product needs one unit of by-product per unit and the daily availability of the by-product is 12 units. According to the marketing department, the sales potential of the first product cannot exceed 7 units. In a competitive market, the first product can be sold at a profit of Rs.6 and the second product at a profit of Rs.10 per unit.  Formulate the problem as a linear programming model. Also determine graphically the feasible region. Identify the redundant constraints if any. 

The table mentioned below shows the “Gross Production of Energy by Two Sources in India from 2010-11 to 2015-16”. Adopt Exponential Smoothing Method. Consider the Alpha (α) values 0.2, 0.5, 0.7 and find out the one that is comparatively good for the prediction. 

Forecast the value for year 2016-17. Year Coal - (Million Tones) Lignite - (Million Tones) 2010-11 532.7 37.73 2011-12 539.95 42.33 2012-13 556.4 46.45 2013-14 565.77 44.27 2014-15 609.18 48.27 2015-16 639.23 43.84

Source: Open Government Data (OGD) Platform India

An organization is interested in the analysis of two products that can be produced from the idle time of labour, machine and investment. It was notified on the investigation that the labour requirement of the first and the second products was 4 and 5 units respectively and the total available man-hours were 48. Only the first product required machine hour utilization of one hour per unit and at present only 10 spare machine hours are available. The second product needs one unit of by-product per unit and the daily availability of the by-product is 12 units. According to the marketing department, the sales potential of the first product cannot exceed 7 units. In a competitive market, the first product can be sold at a profit of Rs.6 and the second product at a profit of Rs.10 per unit.  Formulate the problem as a linear programming model. Also determine graphically the feasible region. Identify the redundant constraints if any.

A large car park has an area of 1400m with space for X cars and Y vans. Each car requires 14m of space and each van requires 35m. on the grid show three inequalities by drawing three lines and shading the unwanted regions