During each of the next two months you can produceas many as 50 units/month of a product at a cost of $12/unitduring month 1 and $15/unit during month 2. The customeris willing to buy as many as 60 units/month during each ofthe next two months. The customer will pay $20/unit duringmonth 1, and $16/unit during month 2. It costs $1/unit tohold a unit in inventory for a month. Formulate a balancedtransportation problem whose solution will tell you how tomaximize profit.
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
During each of the next two months you can produce
as many as 50 units/month of a product at a cost of $12/unit
during month 1 and $15/unit during month 2. The customer
is willing to buy as many as 60 units/month during each of
the next two months. The customer will pay $20/unit during
month 1, and $16/unit during month 2. It costs $1/unit to
hold a unit in inventory for a month. Formulate a balanced
transportation problem whose solution will tell you how to
maximize profit.
Given: The scenario of the production of a product is given.
We need to formulate a balanced transportation problem to maximize profit.
In order to balance this problem we add a dummy supply point, .
We use a negative number with a large absolute value to indicate we can't sell products produced in month on month .
The resulting tableau whose transportation problem needs to be maximized is given by subtracting production and storage costs from revenue.
| Month 1 (M1) | Month 2 (M2) | ||
| M1 | 8 | 3 | 50 |
| M2 | N | 1 | 50 |
| D | 0 | 0 | 20 |
| 60 | 60 |
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