short answer of Math

Ad510 Extra Credit Problem Due 10/26/2018

A company is launching a new product. They have four factories to open and four markets they wish to

sell in. They wish to maximize their profit. The cost to ship units from each factory to each market is

provided in the following table:

Cost to ship/unit

Market

A B C D

F a

ct o

ry 1 $1.50 $1.20 $1.10 $0.90

2 $1.20 $0.75 $1.20 $1.00

3 $1.40 $1.10 $0.90 $1.00

4 $1.00 $1.10 $0.90 $1.20

The cost to produce out of the factories is split into the fixed cost to run the factory each year, and the

variable cost to produce one unit. They are given below, along with the maximum number of units they

can produce in a year:

Factory Fixed Cost/yr Var Cost/unit Max units/yr

1 $130,000 $10 34000

2 $150,000 $9 20000

3 $145,000 $9 23000

4 $190,000 $7 25000

They charge different prices per unit depending on the market they’re selling in. They also know the

yearly demand in each market, as shown in the table below:

Market A B C D

Revenue/unit $51 $48 $47 $45 Market Demand 32000 18000 10000 7500

Use linear programming in solver to determine their optimal strategy, including

a) Which factories to open

b) How many units to ship from each factory to each market

c) What their total profit would be, assuming no additional costs