Consider the Reddy Mikks model

a$)$ Determine the range for the ratio of the unit revenue of exterior paint to the unit revenue of interior paint.

b$)$ If the revenue per ton of exterior paint remains constant at $$5000$ per ton, determine the maximum unit revenue of interior paint that will keep the present optimum solution unchanged.

c$)$ If for marketing reasons the unit revenue of interior paint must be reduced to $$2500,$ will the current optimum production mix change?

d$)$ Used Solver to obtain the sensitivity report for the Reddy Mikks model

i$.$ It is proposed that the availability of raw material $1$ is increase to $30$ tons. Indicate whether the changes will keep the current shadow price?

ii$.$ Determine the value of profit if the availability or raw material $2$ is decrease by $2$ tons.