1. You are provided with the following integer program: max z = 3x + y

s.t.

x + 1.6y 8

5x + 6y 15

x 5.5

x, y 0 and integer

(a) On the graph provided on the following page, use the graphical solution method to identify the feasible points on your graph. (Use the scale 1 by 1 for each small square so that you can visually detect the feasible integer solutions.)

(b) Enumerate the feasible extreme points of the convex hull and calculate their objective values.

Extreme point 1:

Extreme point 2:

Extreme point 3:

Extreme point 4:

Extreme point 5:

Extreme point 6:

(c) Draw an isoprofit line that passes through the point (x = 3, y = 1) and find the direction of optimization.

(d) Provide the optimal solution and optimal objective function value.

Optimal solution: x = -------------- y = ---------------------

Optimal objective value:------------------

Question 2.

Hart Manufacturing makes 3 products. Each product requires manufacturing operations in three departments: A, B, C. The labor requirements (in hour), by department, are as follows:

Department Product 1 Product 2 Product 3

A 1.5 3 2

B 2 1 2.5

C 0.25 0.25 0.25

During the next production period the labor-hours available are 450 in department A, 350 in department B, and 50 in department C.

The profit contributions per unit are $25 for product 1, $28 for product 2, and $30 for product 3.

Develop an all-integer optimization model to determine the production quantity for each product that maximizes the total profit contribution. (Do NOT solve the model.)

Question 3:

An Electrical Company has two manufacturing plants. The cost in dollars of producing an Amplifier at each of the two plants is given below. The cost of producing Q1 Amplifiers at the first plant is:

65Q1 + 4Q1^2 + 90

and the cost of producing Q2 Amplifiers at the second plant is

20Q2 + 2Q2^2 + 120

The company needs to manufacture at least 60 Amplifiers to meet the received orders. Production time required for the Amplifiers at these plants is 6 and 8 hours per unit,

respectively. Currently, there are 260 and 220 hours available at these two plants, respectively. Formulate an optimization model that can be used to find the optimal production quantity of Amplifiers at each of the plant that minimizes the total production cost.

can please explain step by step the 3 quetions