Products of the first and second type have a market value of $9 and $8, respectively.(a) Formulate a linear programming problem that can be used to maximize the daily profit of the company.(b) Suppose that up to 50 hours of overtime assembly labor can be scheduled, at a cost of $7 per hour.Modify the linear program from (a) to incorporate this change. Clearly specify the entire new LP, notjust any changes.Problem 3The XYZ Corporation is undergoing a radical restructuring and needs to hire consultantsto help in several key areas. XYZ has contracts with four consultants (A, B, C, and D). The table belowindicates, for each of the consultants, what they charge per hour and how many hours they have availableto work for XYZ.Consultantrate/hrtotal hours availableA$300/hr60B$250/hr60C$350/hr50D$200/hr40XYZ has four main tasks that need to be completed. The table below indicates how many hours XYZestimates that it would take each consultant to perform each task. If no amount of time is indicated for theconsultant to complete a task, then the consultant cannot perform the task.1

Consultanthrs/task 1hrs/task 2hrs/task 3hrs/task 4A302040B303030C25252525D4040XYZ want to determine how to allocate tasks to consultants at minimum cost. Note that all tasks mustbe completed, but not all consultants need to be used to their full availability.You may also allow con-sultants to split tasks. If they do so, you can assume that each consultant gets a constant fraction of thetask completed per unit of time worked. For example, Consultant A would complete 1/2 of task 1 in 15 hours.(a) Formulate this problem as an LP. Clearly indicate your decision variables, your objective function, andyour constraints.