Suppose you purchase a $4 -per-unit part from a supplier with which you assemble red widegets. On average, you use 50000 units of this part each year. Every time you order this part, you incur a sizable order cost of $800 regardless of the number of parts you order. Your cost of capital is 20% per year.

a)how many parts should you purchase each time you place an order?
b)To satisfy annual demand, how many times per year will you place orders for this part?

Step-by-step explanation:

The data in the question is:

throughput rate R = 50,000 parts/yr, fixed setup cost S = $800, purchasing cost C = $4/part, cost of capital r = 200%/yr, and physical storage cost h = 0%/yr.

Thus the annual unit holding cost is H = (r+h)C = $0.80/part/yr.

The economic order quantity tells us to purchase each time:

The calculation is done in the picture attached

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step-by-step explanation:

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.