Question

Arlo Industries manufactures three types of dog collars: a deluxe model with solid leather and

upgraded leash rings, a standard model using a "leatherette" compound, and a bargain model

that they sell to discount outlets. The profit contributions of these collars are $12 Deluxe, $10

Standard, and $8 Bargain. All collars must be cut, assembled and shipped using three different

production lines. The following table shows the time (in minutes) for each operation:

Production Line

Deluxe

Standard

Bargain

Cutting

10

7

6

Assembly

8

7

6

Shipping

5

5

5

Next month, the company estimates there will be 380 hours available for cutting, 370 hours for

assembly and 400 hours available for shipping. In addition, up to 80 hours of overtime is

available that can be used on either the cutting and/or assembly production lines at a cost of

$20 per hour. The company has already received orders for 1200 deluxe collars, 1000 standard

collars, and 600 bargain collars that must be filled, but believes they can sell as many collars as

they can make. The company is interested in maximizing profit, subject to the constraints listed

above.

Answer 1

Let,

D = number of Deluxe models to produce
S = number of Standard models to produce
B = Number of bargain models to produce
O1 = number of overtime minutes in Cutting and O2 = number of overtime minutes in Assembly operations

Cost of overtime per minute = 20/60 = 0.333333333

Objective is to maximize profit = max 12D+10S+8B-0.333333333*O1-0.333333333*O2

subject to,

10D+7S+6B-O1 <= 22800 (Cutting)
8D+7S+6B-O2 <= 22200 (Assembly)
5D+5S+5B <= 24000 (Shipping)
D >= 1200 (Minimum Deluxe model)
s >= 1000 (Minimum Standard model)
B >= 600 (Minimum Bargain model)

O1+O2 <= 4800 (Available overtime minutes)

D,S,B,O1,O2 >= 0

Solving in solver we get,

D = number of Deluxe models to produce = 1200
S = number of Standard models to produce = 1500
B = Number of bargain models to produce = 600

maximized profit = 32600

Solver screenshot

Solver formula

Solver window