How many of each type should be sold to maximize revenue in the following case:
A local nursery makes two types of fall arrangements. One arrangement uses eight mums and five black-eyed susans. The other arrangement uses six mums and 9 black-eyed susans. The nursery can use no more than 144 mums and 135 black-eyed susans. The first arrangement sells for $49.99 and the second arrangement sells for $38.95. How many of each type should be sold to maximize revenue?
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The local nursery makes two types of fall arrangements. One arrangement uses eight mums and five black-eyed susans. This sells for $49.99. The other arrangement uses six mums and 9 black-eyed susans. This sells for $38.95. The nursery can only use 144 mums and 135 black-eyed susans.
To maximize revenue let the number of arrangements of the the first type be x and that of the second type be y.
The total number of mums used is 8x + 6y and the total number of black-eyed susans is 5x + 9y
8x + 6y <= 144 and 5x + 9y <= 135
It can be seen that the nursery should sell as many of the first arrangement as possible as the revenue earned is higher.
If x = 9 and y = 10 both the conditions are fulfilled and the revenue is 9*49.99 + 10*38.95 = $839.41
If x is made 10, only 9 of y can be made but the revenue is increased to: 10*49.99 + 9*38.95 = $850.45
To maximize revenue the nursery should sell 10 of the first arrangement and 9 of the second arrangement.
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