A manufacturing company that can produce from one up to forty per day, has estimated the following cost and revenue functions where x is the number of units
produced in thousands, and all functions are in thousands of dollars.
C(x) = 160 + 10x and R(x) = x(50 - 1.25x)
(a) Derive the profit function, P(x).
(6) Using algebra, find the break-even values to the nearest thousand units.

Astudent is determining the influence of different types of food on the growth rate of spiders. she feeds one group of spiders two caterpillars twice a week. the other group received similarly-sized beetles twice a week. she records the amount of time required for individuals to reach sexual maturity. her hypothesis is that the spiders feeding on caterpillars will have a faster growth rate because caterpillars have a higher protein content compared to beetles. in this experiment, what is the dependent variable? spiders assigned to different feeding groups. time required to reach sexual maturity number of prey items fed twice a week. growth rates of each group.