ITS Ltd$,$ a leading intelligent transport solutions provider, manufactures environmentally friendly glow$-$in$-$the$-$dark tactile paving pads for city streets and sidewalks. Revenues from product sales are $3$ per street pad and $2$ per sidewalk pad. The production

process requires machine hours, high$-$impact plastics and latex paint. Based on past experience, the daily production of the tactile pads should be made such that the difference between the number of street pad and the number of sidewalk pad is at least $2.$ It takes $6$ machine hours to produce a unit of street pad and $3$ machine hours for a sidewalk pad. Assume that the machine for production of the pads is operated $24$ hours a day. It takes $2$ units of plastics to manufacture a street pad and $3$ units of plastics to manufacture sidewalk pads and the available units of plastics is $12.$ Manufacturing a street pad requires a unit of paint while manufacturing sidewalk path requires $3$ units of paint. Nine units of paint is available.

a$)$ Formulate the optimization problem using the standard format discussed in class.

b$)$ Solve the optimization problem in a$)$ using a graphical approach. Fully lable the graph and show all your work$/$steps$.$

c$)$ Propose a production policy for making tactile pads for transport applications based on the results from b$).$ Include a sensitivity analysis to demonstrate the robustness of your solutions.