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A manufacturer has been selling 1000 television sets a week at $450 each. A market survey indicates that for each $10 worth of rebate offered to buyers, the number of sets sold will increase by 100 per week. (a) Find the demand function. (b) How large a rebate should the company offer buyers in order to maximize its revenue? (c) If its weekly cost function is C(x) = 68000 + 150x, how should the manufacturer set the size of the rebate in order to maximize its prot?
In Utah, a license plate consists of 3 digits followed by 3 letters. The letters I, O, and Q are not used, and each digit or letter may be used more than once. How many different license plates are possible?
a closed box whose length is twice its width is to have a surface of 192 square inches. find the dimensions of a box when the volume is maximum.
Write two expressions--one for labor and one for materials--that can be used to model the labor and materials constraints for the upcoming week.
A triangle drawn on a map has sides of lengths 7 cm, 11 cm, and 14 cm. The shortest of the corresponding real-life distances is 92 km. Find the longest of the real-life distances to the nearest tenth of a kilometer.
Show that if a convergent series of real numbers contains only a finite number of negative terms, then it is absolutely convergent.
Write a linear model which expresses number of people who purchase tickets (N) as a function of the price of a ticket (P). What is the physical meaning of the slope in this linear relationship?
What is the slope of the graph? What does it represent?
Show that the mean value theorem applies or does not apply to the following. f(x)=sqrt(25-x^2), [-4,4]. State the conditions clearly, and, if appropriate, find the c guarenteed by the theorem.
a bank teller. at the end of a dat, she had total of 69 $5 and $10 bills. the total value of the money is $590. how many of each denomination does she have?
It is thought that prehistoric Indians did not take their best tools, pottery, and household items when they visited higher elevations for their summer camps.
One card will be randomly selected from a standard 52-card deck of cards. What is the probability that it will be the jack of hearts?
At point on the ground 70 feet from base of a tree the distance to the top of the tree is 2 feet more than 3 times the height of the tree. What is the height of the tree?
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