Subject $-$ Business optimization analytics:

A linear optimization model of a resource allocation problem $($for maximizing profit.

expressed in dollars, and in which variables are nonnegative, and all constraints are linear inequalities$)$has been solved, and the optimum value of a variable X is X$*=10$tons$.$ Based on this information, which of the following statements $($if any$)$are true?

a$.$The nonnegativity constraint X $20$is binding.

b$.$The nonnegativity constraint X $0$is redundant.

c$.$The reduced cost of variable X is zero.

d$.$The optimum objective value increases by $$10$per unit increase in the objective

coefficient of variable X$,$within its objective coefficient range.

e$.$The reduced cost of variable X is completely determined by its objective and constraint coefficients and by the dual prices.