Give precise formulations for each of the following as constraint satisfaction problems: a. Rectilinear floor-planning: find non-overlapping places in a large rectangle for a number of smaller rectangles. b. Class scheduling: There is a fixed number of professors and classrooms, a list of classes to be offered, and a list of possible time slots for classes. Each professor has a set of classes that he or she can teach. c. Hamiltonian tour: given a network of cities connected by roads, choose an order to visit all cities in a country without repeating any.

1. Write the decision variables in the short form 2. Write the objective function 3. Write the constraints and domain condition

# 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?

Acme Block Company has orders for 80 tons of concrete blocks at three suburban locations as follows: Northwood-25 tons Westwood-45 tons Eastwood-10 tons Acme has two plants, each of which can produce 50 tons per week. Delivery cost per ton from each plant to each suburban location is as follows: Northwood Westwood Eastwood Plant 1 Plant 2 1 24 30 Which one is a correct constraint? A. X11+X12+X13 = 10 OB. X11+X12+X13 ≤ 25 OC X11+X12+X13 = 45 OD. X₁1+X12+X13 ≤ 50 30 40 ہے 40 42

A garment factory makes blouses and dresses. Each blouse gives a profit of$4, while each dress gives a profit of $5. They can sell at most 200 dresses. The number of dresses must be at least 30% of the total number of garments made. Each garment spends time(minutes) on three machines as follows:a) Show the decision variables b) Show the objective functionc) Show the constraints in standard form (i.e. suitable for using Excel’s Solver) d) Solve the linear programming problem by graphing

A linear programming computer package is needed. The Westchester Chamber of Commerce periodically sponsors public service seminars and programs. Currently, promotional plans are under way for this year's program. Advertising alternatives include television, radio, and online. Audience estimates, costs, and maximum media usage limitations are as shown. Constraint Audience per advertisement Cost per advertisement Maximum media usage Radio Online Television Radio 300,000 54,000 120,000 $600 $2,000 10 $300 Online 20 10 To ensure a balanced use of advertising media, radio advertisements must not exceed 50% of the total number of advertisements authorized. In addition, television should account for at least 10% of the total number of advertisements authorized. (a) If the promotional budget is limited to $25,100, how many commercial messages should be run on each medium to maximize total audience contact? Television What is the allocation of the budget among the three media, and what is the…

consider the production scheduling problem of the perfume polly named after a famous celebrity. the manufacturer of the perfume must plan production for the first four months of the year and anticipates a demand of 4000, 5000, 6000, and 4500 gallons in january, february, march, and april, respectively. at the beginning of the year the company has an inventory of 2000 gallons. the company is planning on issuing a new and improved perfume called pollygone in may, so that all polly produced must be sold by the end of april. assume that the production cost for january and february is $5 per gallon and this will rise to $5.5 per gallon in march and april. the company can hold any amount produced in a certain month over to the next month at an inventory cost of $1 per unit. formulate a linear optimization model that will minimize the costs incurred in meeting the demand for polly in the period january through april. assume for simplicity that any amount produced in a given month may be used…

I need explaination and spreadsheet with formulas and step to step interpretation please.....The attached are first two pages of required assisance and below is  the rest of instructions please consider all of them:c. Suppose the CEO says, “Projects 3 and 4 must be undertaken but not both.”Describe the constraint.d. Suppose the CEO says, “Projects 4 cannot be undertaken unless projects 1 and 3also are both undertaken.” Describe the constraints. Hint: You may need to add more than one constraint for this part.3. [45pts] Multi-product Production Planning. Hart Manufacturing makes three products. Each product requires manufacturing operations in three departments: A, B, and C. The labor-hour requirements, by department, are as follows:Department Product 1 Product 2 Product 3A                     1.50           3.00           2.00B                     2.00            1.00         2.50C                     0.25            0.25         0.25During the next production period, the labor-hours…