XYZ Grocery sells two types of soft drinks : the brand name A1 Cola and the cheaper store brand XYZ Cola. The margin of profit on the A1 Cola is about 50 paise per bottle, whereas the XYZ Cola grosses 70 paise per bottle. On the average the store sells 500 bottles of both the Colas a day. Although A1 is a better recognized name, customers tend to buy more of the XYZ brand because it is considerably cheaper. It is estimated that the XYZ brand outsells the A1 brand by a ratio of at least 2:1. However XYZ Grocery sells at least 100 bottles of A1 a day.
(i) How many bottles of each brand should the store carry daily to maximize the total profit ?
(ii) Determine the ratio of the profits per bottle of A1 and XYZ Colas that will keep the solution in (i) unchanged ?