Yummy Creamy is a New York based company that manufactures and distributes ice-cream across tri-state area. The product line includes 2 main flavors – Purple Delight (PD) and Choco- Chips (CC).

Question

Yummy Creamy Is a New York based company that manufactures and distributes Ice-cream across tri-state area. The product line includes 2 main flavors - Purple Delight (PD) and Choco- Chips (CC). On selling 1 unit of each flavor, profit earned is - Flavor Purple Delight (PD) Choco-Chips (CC) Profit per Unit ($) $5.00 $5.30 Given the fact that Yummy Creamy is a newly introduced establishing brand in the area and the nature of the product, they want to limit the stock in the market maximum to: PD-250 and CC - 400 Ingredients required to manufacture each unit of the ice cream is as follows: Flavor PD CC Milk 0.1 0.3 Sugar 0.05 0.1 Cream 0.03 0.02 Total available resources are: Ingredients Milk Sugar Cream Availability 150 130 15 Yummy Creamy needs to determine how many units of each flavor to manufacture to maximize its weekly profit.

Answer 1

So Ank S.,

There are several ways of approaching this problem. The way I would do it is

Draw a cartesian graph, with CC on one axis, and PD on the other. The intercepts are the amounts of each product can be exclusively made with the stated amounts of the ingredients. Compare that to the desired marketed limit, and reduce to the marketed limit if less. Then start graphing the mixed region between: from each extreme, IF one ingredient was expended completely (and not limited by the marketed limit), then there will be a ratio of units of the other product that can be made, as the units of the extremed product are reduced. And there will be a linear function describing the impact on profits as this route is traversed. (If the marketed limit did apply, then there might be some additional product of the other type that could be also made. Then the boundary starts at the point describing that.) These two routes may meet each other, or there may be up to two intermediate segment(s) limited by the third ingredient supply. (you can approach this methodically, by writing functions for the utilization of each ingredient as you traverse a segment. When any ingredient hits zero, another segment must start!) In any event, the maximum profit will be made at one of the segment meeting points -- because the profit is always a linear function on both sides of that. The iso-profit line is then tangent at the desired mix; it has the slope that equalizes the profits between the two products, so the intercept on the CC axis is nearer the origin.

--Hope I haven't discouraged you, construct your 'bounded region" carefully and you should quickly "chip away" at the ice cream market.

--Cheers, --Mr. d.