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To produce x units of a particular commodity, a monopolist has a total cost of C(x) = 2x^2 + 3x + 5. The unit price at which the x units will be sold is p(x) = 5-2x. For what level of production is profit maximized?
a rancher is fencing off a rectangular area with a fixed perimeter of 76. What dimensions would yield the maximum area?
A 28-year-old man pays $157 for a one-year life insurance policy with coverage of $140,000. If the probability that he will live through the year is 0.9994, what is the expected value for the insurance policy?
Find the gradient of the function and the maximum value of the directional derivative at the indicated point:
A consumer is trying to decide between two long-distance calling plans. The first charges a flat rate of 10¢ ($0.10) per minute,
establish the method of Lagrange multipliers in the case where we wish to find the extreme values of F(x,y,z) subject to the two constraint conditions G(x,y,z)=0, H(x,y,z)=0
in triangle MNO, angle M is equal to angle N, and angle O is 5 more than three times angle N. what is the measure of each angle?
A bookstore has an annual demand for 40,000 copies of a best-selling book. It costs $0.90 to store one copy for one year, and it costs $15 to place an order. Find the optimum number of copies per order.
The population of a community is known to increase at a rate proportional to the number of people present at time t
a spherical tank has a capacity of 750 gallons. using the fact that one gallon is about .1337 ft^3, find the radius of the tank to the nearest hundredth of a foot.
How fast is the object moving 9s after being thrown?
Miranda's finanical aid stipulates that her tuition not exceed $1500. If her college charges a $45 registration fee plus $275 per course, what is the greatest number of courses for which Miranda can register?
Let G be k-critical graph with respect to vertex-arboricity (k>=3). Prove that for each vertex v of G, the graph G-v is not (k-1)-critical with respect to vertex-arboricity.
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