# Integer Problem

I need to verify my work and need help with work on Exercises 4, 5, 6, 7 from attached PDF file and Excel file. Please help soon. Please find the attached zip file for all the related files.

4. The Big Bang Novelty Company makes three basic types of noise-makers: Toot, Wheet,

and Honk. A Toot can be made in 30 minutes and has a feather attached to it. A

Wheet requires 20 minutes, has two feathers, and is sprinkled with 0.5 ounces of sequin

powder. The Honk requires 30 minutes, three feathers, and 1 ounce of sequin powder.

The unit profits are $0.45 per Toot, $0.55 per Wheet, and $0.70 per Honk. The

following resources are available: 4800 minutes of labor, 90 ounces of sequin powder,

and 360 feathers.

? If the company produces any Toots, it incurs a fixed cost of $15.

? If the company produces any Wheets, it incurs a fixed cost of $25.

? If the company produces any Honks, it incurs a fixed cost of $10.

The company believes that the maximum numbers of Toots, Wheets and Honks it can

sell are 200, 500 and 300 respectively. Formulate an ILP for determining the product

mix that maximizes total profit subject to the resource constraints.

5. A manufacturing company produces three products each of which must be processed

on two machines. The processing times for each product on each machine along with

the maximum available time on the machines per week is given in the table below:

Machine Product 1 Product 2 Product 3 Maximum Available

1 4 hours 6 hours 1 hour 2000 hours

2 2 hours 2 hours 3 hours 1500 hours

There is a fixed cost associated with the production of each product. The table below

shows the fixed costs along with unit contribution from the sale of a unit of each

product.

Product Fixed Costs Unit Contribution

1 $100 $5

2 $150 $7

3 $ 75 $4

Formulate an integer programming model to maximize the profit after accounting for

the fixed costs.

B. Madhu Rao 6

6. A corporation is planning to produce a new product, and is considering six possible sites

for its manufacturing plants. The plants that are built must serve four customer service

centers. The accompanying table shows expected monthly demand for each customer

service center, and potential monthly capacity for each possible manufacturing plant.

Also shown are unit production and transportation costs for each possible plant/service

center route, together with fixed costs per month for each possible plant. These cost

figures are all in dollars.

Customer service center

1 2 3 4 Fixed Potential

Plant variable cost per unit costs supply

1 10 12 13 17 $3,000 700

2 11 9 10 14 $3,500 750

3 15 12 8 10 $2,600 650

4 18 15 13 9 $2,100 550

5 13 16 14 12 $3,900 800

6 18 11 8 16 $2,800 600

Demand 800 600 700 500

This corporation wants to select plant sites and develop a transportation policy so

that total monthly costs are as small as possible, subject to the requirement that all

demand must be met. Formulate the mathematical programming problem that must

be solved.

7. A firm is considering three different products for the upcoming planning horizon. The

pertinent information is given in the table below.

Product Raw Material Direct Labor Revenues

(lbs) (hours)

1 10 5 $15

2 15 4 $12

3 20 7 $20

There is 500,000 lbs. of raw material available. The variable cost of direct labor is $10

per hour. The fixed cost of the production facility is based on the amount of labor

(a function of people working in the production facility and their equipment needs).

The Industrial Engineering department estimates the following steps of fixed costs as

a function of the direct labor requirements in the production process.

Fixed Costs ($) Direct labor Requirement

200,000 up to 30,000 hr.

300,000 30,000-50,000 hr.

500,000 50,000-100,000 hr.

Formulate an IP model to determine the optimal product mix.