In Example $4\mathrm{.}3-2$:

a$.$ Suppose that TOYCO is studying the possibility of introducing a fourth toy: fire trucks. The assembly does not make use of operation $1.$ Its unit assembly times on operations $2$ and $3$ are $1$ and $3$ minutes, respectively. The revenue per unit is $$4.$ Would you advise TOYCO to introduce the new product? Justify your answer.

b$.$ Suppose that TOYCO wants to change the capacities of the three operations to $300,800,$ and $200$ minutes, respectively. Use post$-$optimal analysis, if needed, to determine the optimum solution.

c$.$ Suppose the fourth operation has the following specifications: The maximum production rate based on $480$ minutes a day is $120$ units of product $1,480$ units of product $2,$ or $240$ units of product $3.$ Determine the optimal solution, assuming that the daily capacity is limited to $548$ minutes.

d$.$ Investigate the optimality of the TOYCO solution considering $z=4x_1+2x_2+8x_3.$ Use post$-$optimal analysis, if needed, to determine the new optimum.

e$.$ Suppose that a new toy $($fire engine$)$ requires $3,2,$ and $4$ minutes, respectively, on operations $1,2,$ and $3.$ Determine the optimal solution when the revenue per unit is given by $$10.$