The revenue function R(x) and the cost function C(x) for a particular product are given. These functions are valid only for the specified range of values. Find the number of units that must be produced to break even. R(x) = 200x-x²; C(x) = 65x+2750; 0 ≤ x ≤ 100
Accepted Solution
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Answer:The number of units that must be produced to break even is 25.Step-by-step explanation:Given : The revenue function R(x) and the cost function C(x) for a particular product are given. These functions are valid only for the specified range of values. [tex]R(x) = 200x-x^2[/tex] ; [tex]C(x) = 65x+2750[/tex] ; [tex]0 \leq x \leq100[/tex]To find : The number of units that must be produced to break even ?Solution : We know that,At break even the cost price and revenue became equal.So, [tex]C(x)=R(x)[/tex]Substitute the values,[tex]65x+2750=200x-x^2[/tex][tex]65x-200x+x^2+2750=0[/tex][tex]x^2-135x+2750=0[/tex]Applying middle term split,[tex]x^2-110x-25x+2750=0[/tex][tex]x(x-110)-25(x-110)=0[/tex][tex](x-110)(x-25)=0[/tex]Either x=110 or x=25Since, [tex]0 \leq x \leq100[/tex]The value of x is 25.Therefore, the number of units that must be produced to break even is 25.