Chapter 16.4, Problem 17P

The Pretty Flower Company starts plants from seed and sells the seedlings to nurseries. They know from experience that about 60% of the calla lily seeds they plant will sprout and become a seedling. Each calla lily seed costs 20 cents, and a pot containing at least one sprouted calla lily seedling can be sold for $2.00. Pots that don’t contain a sprouted seedling must be thrown out. The company figures that costs for a pot, potting soil, water, fertilizer, fungicide and labor are $0.30 per pot (whether or not a seed in the pot sprouts). The Pretty Flower Company is debating between planting 1 or 2 seeds per pot. Help them figure out which choice will be more profitable by working through the following problems:

a. Suppose the Pretty Flower Company plants 1 calla lily seed in each of 100 pots. Using the previous information, approximately how much profit should the Pretty Flower Company expect to make on these 100 pots? Profit is income minus expenses.
b. Now suppose that the Pretty Flower Company plants 2calla lily seeds (1 on the left, 1 on the right) in each ofloo pots. Assume that whether or not the left seedsprouts has no influence on whether or not the right seedsprouts. So, the right seed will still sprout in about 60% ofthe pots in which the left seed does not sprout. Explainwhy the Pretty Flower Company should expect about 84of the 100 pots to sprout at least 1 seed.
c. Using part (b), determine how much profit the PrettyFlower Company should expect to make on 100 pots if 2calla lily seeds are planted per pot. Compare your answerwith part (a). Which is expected to be more profitable: 1seed or 2 seeds per pot?
d. What if calla lily seeds cost 50 cents each instead of 20cents each (but everything else stays the same)? Nowwhich is expected to be more profitable: 1 seed or 2seeds per pot?