> with(plots); -1
 

> `:=`(P, proc (n) options operator, arrow; `*`(`+`(80000, `-`(`*`(5000, `*`(n)))), `*`(`+`(1.50, `*`(.1, `*`(n))))) end proc); 1
 

proc (n) options operator, arrow; `*`(`+`(80000, `-`(`*`(5000, `*`(n)))), `*`(`+`(1.50, `*`(.1, `*`(n))))) end proc (1)
 

> P(n); 1
 

`*`(`+`(80000, `-`(`*`(5000, `*`(n)))), `*`(`+`(1.50, `*`(.1, `*`(n))))) (2)
 

> plot(P(n), n = 0 .. 5); 1
 

Plot_2d
 

> `:=`(dPdn, diff(P(n), n)); 1
 

`+`(500.00, `-`(`*`(1000.0, `*`(n)))) (3)
 

> `:=`(nstar, solve(dPdn = 0, n)); 1
 

.5000000000 (4)
 

> `+`(1.50, `*`(.10, `*`(nstar))); 1
 

1.550000000 (5)
 

> P(.5); 1
 

120125.000 (6)
 

> `:=`(P, proc (n) options operator, arrow; `*`(`+`(80000, `-`(`*`(alpha, `*`(n)))), `*`(`+`(1.50, `*`(.1, `*`(n))))) end proc); 1
 

proc (n) options operator, arrow; `*`(`+`(80000, `-`(`*`(alpha, `*`(n)))), `*`(`+`(1.50, `*`(.1, `*`(n))))) end proc (7)
 

> `:=`(dPdn, diff(P(n), n)); 1
 

`+`(`-`(`*`(alpha, `*`(`+`(1.50, `*`(.1, `*`(n)))))), 8000.0, `-`(`*`(.1, `*`(alpha, `*`(n))))) (8)
 

> `:=`(nstar, solve(dPdn = 0, n)); 1
 

`+`(`-`(`/`(`*`(2.500000000, `*`(`+`(`*`(3., `*`(alpha)), `-`(16000.)))), `*`(alpha)))) (9)
 

> assign(alpha = 3000); 1; nstar; 1; `+`(1.50, `*`(.10, `*`(nstar))); 1; P(nstar); 1
 

 

 

5.833333332
2.083333333
130208.3333 (10)
 

> unassign('alpha'); 1
 

> assign(alpha = 4000); 1; nstar; 1; `+`(1.50, `*`(.10, `*`(nstar))); 1; P(nstar); 1
 

 

 

2.500000000
1.750000000
122500.0000 (11)
 

> unassign('alpha'); 1
 

> assign(alpha = 5000); 1; nstar; 1; `+`(1.50, `*`(.10, `*`(nstar))); 1; P(nstar); 1
 

 

 

.5000000000
1.550000000
120125.0000 (12)
 

> unassign('alpha'); 1
 

> assign(alpha = 6000); 1; nstar; 1; `+`(1.50, `*`(.10, `*`(nstar))); 1; P(nstar); 1
 

 

 

-.8333333332
1.416666667
120416.6667 (13)
 

> unassign('alpha'); 1
 

> assign(alpha = 7000); 1; nstar; 1; `+`(1.50, `*`(.10, `*`(nstar))); 1; P(nstar); 1
 

 

 

-1.785714286
1.321428571
122232.1428 (14)
 

> unassign('alpha'); 1
 

> `:=`(P, proc (n) options operator, arrow; `*`(`+`(80000, `-`(`*`(alpha, `*`(n)))), `*`(`+`(1.50, `*`(.1, `*`(n))))) end proc); 1
 

proc (n) options operator, arrow; `*`(`+`(80000, `-`(`*`(alpha, `*`(n)))), `*`(`+`(1.50, `*`(.1, `*`(n))))) end proc (15)
 

> `:=`(dPdn, diff(P(n), n)); 1
 

`+`(`-`(`*`(alpha, `*`(`+`(1.50, `*`(.1, `*`(n)))))), 8000.0, `-`(`*`(.1, `*`(alpha, `*`(n))))) (16)
 

> `:=`(nstar, solve(dPdn = 0, n)); 1
 

`+`(`-`(`/`(`*`(2.500000000, `*`(`+`(`*`(3., `*`(alpha)), `-`(16000.)))), `*`(alpha)))) (17)
 

> `:=`(pstar, `+`(1.50, `*`(.1, `*`(nstar)))); 1
 

`+`(1.50, `-`(`/`(`*`(.2500000000, `*`(`+`(`*`(3., `*`(alpha)), `-`(16000.)))), `*`(alpha)))) (18)
 

> `:=`(dpstardalpha, diff(pstar, alpha)); 1
 

`+`(`-`(`/`(`*`(.7500000000), `*`(alpha))), `/`(`*`(.2500000000, `*`(`+`(`*`(3., `*`(alpha)), `-`(16000.)))), `*`(`^`(alpha, 2)))) (19)
 

> `:=`(S, `/`(`*`(dpstardalpha, `*`(alpha)), `*`(pstar))); 1
 

`/`(`*`(`+`(`-`(`/`(`*`(.7500000000), `*`(alpha))), `/`(`*`(.2500000000, `*`(`+`(`*`(3., `*`(alpha)), `-`(16000.)))), `*`(`^`(alpha, 2)))), `*`(alpha)), `*`(`+`(1.50, `-`(`/`(`*`(.2500000000, `*`(`+`(... (20)
 

> assign(alpha = 5000); 1; S; 1
 

-.5161290323 (21)
 

>