Collecting the used products (Model C)

$f^{T *} = \frac{- 4 c_{r} k - 8 c_{r} γ + 2 k γ + 2 c_{n} k γ + 8 γ^{2} + 4 c_{r} γ^{2} - 3 γ^{3} - c_{n} γ^{3}}{2 (2 k + 8 γ - 3 γ^{2})}$

$q_{n}^{T *} = \frac{2 k - 2 c_{n} k + 8 γ - 8 c_{n} γ + 2 c_{r} γ - 3 γ^{3} + c_{n} γ^{2}}{2 (2 k + 8 γ - 3 γ^{2})}$

$q_{r}^{T *} = \frac{2 (c_{n} γ - c_{r})}{2 k + 8 γ - 3 γ^{2}}$

$Π_{m}^{T *} = \frac{1}{4} {(1 - c_{n})}^{2} + \frac{{(c_{n} γ - c_{r})}^{2} (2 k + 4 γ - 3 γ^{2})}{{(2 k - 8 γ + 3 γ^{2})}^{2}}$

$Π_{3 p}^{T *} = \frac{4 γ {(c_{n} γ - c_{r})}^{2}}{{(2 k + 8 γ - 3 γ^{2})}^{2}}$

$Π_{t}^{T *} = \frac{1}{4} {(1 - c_{n})}^{2} + \frac{{(c_{n} γ - c_{r})}^{2}}{2 k + 8 γ - 3 γ^{2}}$

Remarketing the remanufactured products (Model R)

$w^{R *} = \frac{γ (- 2 c_{r} - c_{n} k - 2 c_{n} γ + 2 c_{r} γ + 2 c_{r} γ^{2})}{- k - 4 γ + 4 γ^{2}}$

$q_{n}^{R *} = \frac{k - c_{n} k + 4 γ - 4 c_{n} γ + 2 c_{r} γ - 4 γ^{2} + 2 c_{n} γ^{2}}{2 (k + 4 γ - 4 γ^{2})}$

$q_{r}^{R *} = \frac{c_{n} γ - c_{r}}{k + 4 γ - 4 γ^{2}}$

$Π_{m}^{R *} = \frac{1}{4} {(1 - c_{n})}^{2} + \frac{{(c_{n} γ - c_{r})}^{2} (- k - 2 γ + 2 γ^{2})}{2 {(k + 4 γ - 4 γ^{2})}^{2}}$

$Π_{3 p}^{R *} = \frac{{(c_{n} γ - c_{r})}^{2}}{2 (k + 4 γ - 4 γ^{2})}$

$Π_{t}^{R *} = \frac{1}{4} {(1 - c_{n})}^{2} + \frac{γ (γ - 1) {(c_{n} γ - c_{r})}^{2}}{{(k + 4 γ - 4 γ^{2})}^{2}}$