If a worker wants to pack 200 newly harvested mangoes at average size of 3"x2" in delivery boxes .To optimize the cost and profit in packaging , the mangoes must be properly packed in boxes of similar sizes. To systemize counting , there must also be equal number of mangoes in boxes .He must also consider that mango fruits are fragile and must be packed properly to aoid spoilage and damage to the fruits . What he will do ?
The question as it is has a large number of solutions. In general, optimization problems have an objective function, such as minimum cost, minimum surface area, etc. and subject to constraints, such as maximum number of fruits per box, or maximum sizes, etc.
An example solution without constraints could be
10 boxes of 20 mangoes each, with 4 rows of 5 mangoes in each box.
To optimize the cost and profit in packaging the mangoes, the worker must ensure proper packing in boxes of similar sizes. Here's a step-by-step guide on what he can do:
1. Determine the size of the delivery boxes: The worker needs to decide on the size of the delivery boxes that will accommodate the mangoes. Since the average size of the mangoes is 3"x2", he should select a box size that provides enough room for the mangoes without excessive empty space.
2. Calculate the number of mangoes per box: Since the worker wants to have an equal number of mangoes in each box, he needs to divide the total number of mangoes (200) by the desired number of mangoes per box. It's important to consider the box size and the fragility of the mangoes while determining the optimal number.
3. Arrange the mangoes carefully: The worker should handle the mangoes with care to prevent spoilage and damage. He can place a layer of cushioning material (such as paper, bubble wrap, or foam) at the bottom of the box to protect the mangoes. Then, he should place the mangoes in a single layer, making sure to leave some space between them to avoid excess pressure.
4. Add dividers if needed: If the worker feels that the mangoes need additional support or to prevent them from shifting during transportation, he can consider adding dividers or inserts in the box. These dividers can be made of cardboard or foam and should be placed strategically to create separate compartments for each mango, further protecting them from damage.
5. Repeat the process: The worker should repeat the packing process for each box until all the mangoes are properly packed. It's crucial to ensure consistency in packing and maintaining the same number of mangoes in each box.
By following these steps, the worker can systemize the counting, optimize cost, and minimize the risk of spoilage or damage to the mangoes during transportation.