solve the following problems (based on problems in the text, Blanchard and Fabry
ID: 2747233 • Letter: S
Question
solve the following problems (based on problems in the text, Blanchard and Fabrycky, “Systems Engineering and Analysis”, Prentice-Hall, 5th Edition, 2011) . A processing centre has the capacity to assemble 500,000 units per year. At present it is operating at 75% of capacity. The annual income is $500,000. The annual fixed cost is $125,000 and the variable cost $0.50 per unit assembled. i) What is the annual profit or loss of the centre? ii) At what volume of output does the centre break even? iii) What will be the profit or loss at 70%, 80% and 90% of capacity on the basis of constant income per unit and constant variable cost per unit?Explanation / Answer
Capacity= 500,000
Operating capacity= 75% of 500,000 =375,000
Annual income= 500,000/375,000= 1.33 per unit
1. Profit = 500,000-(125,000 +375,000 X 0.5)= 187,500
2. Break even output= Fixed cost/(unit price-unit variable cost) = 125000/(1.333-0.5)= 150,000
Any output less than 150,000 will lead to loss
3. Let T be the percentage of operation, then
Profit is given by 1.33(500,000T)-(125,000+0.5(500,000T)) =5/6(500,000T)-125,000
For T= 70%, we get profit as 166,667
For T= 80%, we get 208,333
For T=90%, we get 250,000
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