Text erkannt:
Gesamthachfrage in Gewinnoptimum
\( \begin{aligned} D(p) &=-6,4 p+3080 \\ D^{-1}(q) &=p=-\frac{1}{6,4} \cdot q+481,25 \\ \pi(q) &=R(q)-C(q) \\ &=p \cdot q-C(q) \\ &=D^{-1}(q) \cdot q(q) \\ \pi(q) &=\left(-\frac{1}{6,4} q+481,25\right) \cdot q-C(q) \\ &=-\frac{1}{6,4} \cdot q^{2}+481,25 q-\left(0,001 \cdot q^{3}+0,001 \cdot q^{2}+2,5 q+\right.\\ &=-0,001 \cdot q^{3}-0,166250 \cdot q^{2}+478,75 \cdot q-13500^{13500} \\ \pi(q) &=-0,001 q^{3}-0,166250 q^{2}+478,75 \cdot q-13500 \\ \pi^{\prime}(q) &=-0,003 q^{2}-0,3325 q+478,25 \\ 0=\pi 1^{\prime}(q) \\ x_{1}=&-458,51+\text { Gesamthachprage im } \\ x_{2}=347,6809 \end{aligned} \)
Pres in gewinnoptimum
\( \begin{array}{l} D^{-1}(q): p=\frac{1}{6,4} \cdot\left(x_{2}\right)+481,25 \\ 347,6809=-6,4+3080 \\ p=426,92 \\ \pi\left(x_{2}\right)=-\pi(347,68)=90653,39 \\ \text { kosten peartform } 347,168: 27=12,877 \sim 1 \end{array} \)
