# 17. Scott and Associates, Inc., is an accounting firm that has three new clients. Project leaders will be assigned to the three clients. Based on the different backgrounds and experiences of the leaders, the various leader-client assignments differ in terms of projected completion times. The possible assignments and the estimated completion times in days are as follows:                                                       ClientProject Leader                        1         2           3Jackson                                   10       16         32Ellis                                          14       22        40Smith                                       22       24        34 a. How many constraints are there in the linear program (not including the non-negativity constraints)?b. What is the total completion time in days?

Suppose a certain manufacturing company produces connecting rods for 4- and 6-cylinder automobile engines using the same production line. The cost required to set up the production line to produce the 4-cylinder connecting rods is $2,400, and the cost required to set up the production line for the 6-cylinder connecting rods is $3,600. Manufacturing costs are $14 for each 4-cylinder connecting rod and $19 for each 6-cylinder connecting rod. Hawkins makes a decision at the end of each week as to which product will be manufactured the following week. If a production changeover is necessary from one week to the next, the weekend is used to reconfigure the production line. Once the line has been set up, the weekly production capacities are 5,000 6-cylinder connecting rods and 7,000 4-cylinder connecting rods. Let 56 = 1 if the production line is set up to produce the 6-cylinder connecting rods; 0 if otherwise (a) Using the decision variables x4 and s, write a constraint that limits next…

There are three factories located at AR, IN, and TX respectively. From these locations, a certain commodity is to be delivered to each of the two warehouses situated at A and B. The revenue per commodity item is $10. The weekly demand of the warehouse A and B are respectively 50 and 35 units of the commodity while the production capacity of the factories at AR, IN, and TX are respectively 28, 22, and 35 units. The cost of transportation per unit is given as belows.   Cost Warehouse A Warehouse B AR 5 3 IN 6 6 TX 2 4   To maintain a good relationship with all the factories, warehouse B requires that it receives at least 40% of its product from factory in TX. Realize that it is making good profit in warehouse A, AR requires that at least 35% of its product shipped to warehouse A. Formulate (without solving) a linear programming problem to maximize the profit.

A law form specialized in the issuance of insurance policies covering large commercial real estate projects. The projects fall into two categories: shopping centers, and medical complexes. The typical work involved in each transaction is quite predictable and repetitive. The time requirements (unit loads) for preparing a standard contract of each type are given in the following table. Also listed are the number of professionals of each type and the number of available hours per professional per day (the rest of time is taken by other office activities):   Unit load Shopping (hour/contract) Unit load Medical (hour/contract)  No. of professionals Hours available (hours/professional /day) Paralegal 4 6 4 6 Tax lawyer 1 3 3 8 Senior partner 1 1 2 4  For the month of Feb 2023, the firm has generated the 150 orders, 75 of each type. Assume one month equals 20 days.       QUESTIONS What is the effective capacity of the process…