WebR — Maximização de Lucro: P = CMg

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# ============================================
# Maximizacao de Lucro: P = CMg
# CT(q) = CF + a*q + b*q^2 + c*q^3
# ============================================

# --- Parametros (altere e re-execute!) ---
CF <- 50       # custo fixo
a  <- 2        # coef. linear
b  <- 0.5      # coef. quadratico
p  <- 12       # preco de mercado

# --- Funcoes de custo ---
CT   <- function(q) CF + a*q + b*q^2
CV   <- function(q) a*q + b*q^2
CMg  <- function(q) a + 2*b*q
CMe  <- function(q) CF/q + a + b*q
CVMe <- function(q) a + b*q

# --- Quantidade otima: p = CMg ---
q_star <- (p - a) / (2*b)

# --- Verificacoes ---
cso <- 2*b  # d(CMg)/dq = 2b > 0? (CSO)
cvme_min <- a  # CVMe minimo (CVMe = a + bq, min em q -> 0+)
cme_min_q <- sqrt(CF / b)
cme_min <- CMe(cme_min_q)

lucro <- p * q_star - CT(q_star)
ep <- p * q_star - CV(q_star)  # excedente do produtor

cat("====== MAXIMIZACAO DE LUCRO ======\n")
cat("CT(q) =", CF, "+", a, "q +", b, "q^2\n")
cat("Preco de mercado: p =", p, "\n\n")

cat("--- CPO: p = CMg ---\n")
cat("q* =", round(q_star, 2), "\n")
cat("CMg(q*) =", round(CMg(q_star), 2), " = p =", p, " OK!\n\n")

cat("--- CSO: CMg crescente? ---\n")
cat("d(CMg)/dq =", cso)
if (cso > 0) cat("  > 0 => MAXIMO confirmado\n\n") else cat("  <= 0 => CUIDADO!\n\n")

cat("--- Decisao de operar ---\n")
cat("CVMe_min =", round(cvme_min, 2), "\n")
cat("p =", p, ifelse(p >= cvme_min, " >= CVMe_min => OPERAR", " < CVMe_min => FECHAR"), "\n\n")

cat("--- Resultados ---\n")
cat("RT = p*q* =", round(p * q_star, 2), "\n")
cat("CT(q*) =", round(CT(q_star), 2), "\n")
cat("Lucro =", round(lucro, 2), "\n")
cat("Excedente do produtor = RT - CV =", round(ep, 2), "\n")

if (lucro > 0) {
  cat("\n=> LUCRO POSITIVO: p > CMe_min =", round(cme_min, 2), "\n")
} else if (lucro == 0) {
  cat("\n=> LUCRO ZERO (break-even)\n")
} else {
  cat("\n=> PREJUIZO, mas operar perde menos que fechar\n")
  cat("   Se fechasse: lucro = -CF = -", CF, "\n")
  cat("   Operando: lucro =", round(lucro, 2), " > -", CF, "\n")
}

# --- Grafico ---
par(mar = c(4.5, 4.5, 3, 2), bg = "#f8f9fa")
q_seq <- seq(0.1, q_star * 2.5, length = 500)

plot(q_seq, CMg(q_seq), type = "l", lwd = 3, col = "#dc3545",
     xlab = "q", ylab = "$/unidade",
     main = paste0("Maximizacao de lucro: p = ", p),
     ylim = c(0, max(CMe(q_seq[q_seq > 1])) * 1.2), cex.lab = 1.1)
lines(q_seq, CMe(q_seq), lwd = 2, col = "#0d6efd")
lines(q_seq, CVMe(q_seq), lwd = 2, col = "#198754", lty = 2)
abline(h = p, col = "#fd7e14", lwd = 2, lty = 1)

# Retangulo de lucro
if (lucro > 0) {
  rect(0, CMe(q_star), q_star, p, col = rgb(0.05, 0.43, 0.09, 0.15), border = NA)
} else if (lucro < 0) {
  rect(0, p, q_star, CMe(q_star), col = rgb(0.86, 0.21, 0.27, 0.15), border = NA)
}

# Ponto otimo
points(q_star, p, pch = 19, col = "#dc3545", cex = 2)
text(q_star, p, paste0("  q*=", round(q_star, 1), "\n  lucro=", round(lucro, 1)),
     pos = 4, cex = 0.85, font = 2, col = "#dc3545")

# Ponto de fechamento
points(0.5, cvme_min, pch = 17, col = "#fd7e14", cex = 1.5)
text(0.5, cvme_min, paste0("  Shutdown\n  p_min=", round(cvme_min, 1)),
     pos = 4, cex = 0.75, col = "#fd7e14")

legend("topright",
       legend = c("CMg", "CMe", "CVMe", paste0("p = ", p)),
       col = c("#dc3545", "#0d6efd", "#198754", "#fd7e14"),
       lwd = c(3, 2, 2, 2), lty = c(1, 1, 2, 1),
       cex = 0.8, bg = "white")

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