Problem$2$ ACP. Able City Planning $($ACP$)$ is considering to design a pedestrian overpass. The company allocates $150$ hours to complete the project. Three ACP designers are available for assignment to this project: Elisabeth, a senior designer and team leader, David, a senior designer and Suri, a junior designer. Management specified that Elisabeth must be assigned at least $40\%$ of the total number of hours assigned to the two senior designers. To provide designing experience, Suri must be assigned at least $15\%$ of the total project time. However, the number of hours assigned to Suri must not exceed $25\%$ of the total number of hours assigned to the two senior designers. Elizabeth has only a maximum of $50$ hours available to work on this project. Pay per hour are the following: $$30$ for Elizabeth, $$25$ for David, and $$18$ for Suri. ACP wants to minimize total cost of the project.

Provide decision variable$($s$)$ X$1...$Xn with notation identified and a Linear Programming Model to minimize the total cost of the project.

Provide the optimal solution and the corresponding objective function values. Write the optimal solution $($the values of the decision variables$)$ on first line of text and the value of the objective function at the optimal solution on the second line.