An organization produces two products, X and Y. The materials used for the production of both products are limited to 500 kilograms (kg) per month. All other resources are unlimited and their costs are fixed. Individual product details are as follows:
Product X -
Product Y -
Selling price per unit -
$10
$13
Materials per unit (at $1/kg)
2 kg
6 kg
Monthly demand -
100 units
120 units
In order to maximize profit, how much of product Y should the organization produce each month?
The organization has a total of 500 kg of materials available each month. To maximize profit, we need to allocate these materials efficiently between products X and Y. Product X requires 2 kg of material per unit and has a demand of 100 units, which equates to 200 kg of materials. This leaves 300 kg of materials for product Y. Since product Y requires 6 kg of material per unit, the organization can produce 50 units of product Y (300 kg / 6 kg per unit = 50 units).
it looks like product X demand should be fulfilled, so 100 units times 2 kg of materials = 200 kg of materials used. Materials left counts 300 kg which gives 50 units (300/6) of product Y.
This makes sense. Thank you
If the objective is to maximize profit, this formula gives only $5900 which is [(100 x 2 x 10) + (50 x 6 x 13)] whereas, if production meets a demand of 10 units of x and 80 units of y, the profit is $6440 which is [(10 x 2 x 10) + (80 x 6 x 13)]
Even with option B (60 units of Y), the profit is $6080.
Badly-formatted problem
Pls explain the answer
we get 10-2 = 8 margin from X and 13-6=7 for Y, it means we should maximize product X and then produce product Y