given P(N)= 10N-N2-6.34
4,500 widgets
=>N=4.5
Expression for the profit at a production level of 4,500 widgets
is P(4.5)
P(4.5)= 10(4.5)-4.52-6.34
=>P(4.5)= 45-22.5-6.34
=>P(4.5)= 18.41
value is 18.41
profit at a production level of 4,500 widgets is 18.41 thousand
dollars
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fixed cost =P(0)
=>fixed cost =10(0)-(0)2-6.34
=>fixed cost =-6.34 thousand dollars
-----------------------------------------
at breakeven profit is zero
=>10N-N2-6.34=0
=>N2-10N=-6.34
=>N2-2(5)N+52=52-6.34
=>(N-5)2=18.66
=>N-5=-(18.66)1/2
=>N=5-(18.66)1/2
=>N=0.6802777867.......thousand widgets
break-even point is 680 widgets
--------------------------------------------
P(N)= 10N-N2-6.34
=>P(N)= -(N2-10N)-6.34
=>P(N)=
-(N2-2(5)N+52-52)-6.34
=>P(N)= -(N-5)2+52-6.34
=>P(N)= -(N-5)2+18.66
maximum profit is 18.66 thousand dollars which occurs when 5000
widgets are produced in an year
