Instructions: Model the following problem and submit your LP on Monday 11/5/2020 at
11:55pm. Start your code before your lab session and utilize the session to ask questions and get
help for code debugging. Clearly indicate in a separate word document your optimal solution.
Submit all of your code files along with your final answers document in one zip folder onto elearning
on Thursday 14/5/2020 at 11:55pm.
A company has three factories, a distribution center, and five stores. They produce their products
in the factory, ship them to the distribution center for sorting, and then the products are shipped
from the distribution center to the stores to stock up the shelves. Each factory is responsible for
producing one product only. Factory 1 can produce a maximum of 10K products, factory 2 can
produce a maximum of 20K products, and factory 3 can produce a maximum of 15K products in
a cycle. The distribution center’s total capacity is 40K products total. The shipping costs from
factories to the distribution center are a $1000 at fee plus the cost of shipping per product shipped,
and Table 7 summarizes the shipping cost per product from each factory to the distribution center.
Table 1: Shipping cost from factory to the distribution center
Factory 1 Factory 2 Factory 3
$600 $700 $1000
Each store requires a mix of the three products with a minimum required number of products to be
received from the factories every cycle (Table 2). The shipping cost from the distribution center
to the stores are a at $1000 at fee plus the cost of shipping per product shipped, and Table 3
summarizes the shipping cost per product from the distribution center to each store. However, if
the store is receiving more than a total of 8K of products, they incur a constant cost of $1,000 for
the extra shipping trucks. Finally, because where the stores are located, and supply and demand
forces, each item sells differently in different stores. The selling price is detailed in Table 4. The
company wants to maximize their net profit.
Table 2: Minimum order from each product for each store
Store 1 Store 2 Store 3 Store 4 Store 5
Product 1 2000 1000 3000 1000 1000
Product 2 4000 3000 4000 2000 2000
Product 3 2000 2000 3000 1000 1000
Table 3: Transportation cost from distribution center to store per item
Store 1 Store 2 Store 3 Store 4 Store 5
$8 $10 $7 $6 $9
Table 4: Selling price of each product in each store, $
Store 1 Store 2 Store 3 Store 4 Store 5
Product 1 170 175 180 165 160
Product 2 160 155 165 150 155
Product 3 140 130 135 145 130
Model the problem as a linear program. Fully define any variable or parameter that you use.
Solve the problem using software to obtain an optimal solution.
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