Find two positive numbers satisfying the given requirements. the sum of the first and twice the second is 160 and the product is a maximum.

Two positive numbers x, y, such that x + 2y = 160.

The values of x and y that maximize xy.

The product will be maximized when its derivative is zero. We can write the product in terms of a single variable to make solution easier.

... y = (160 -x)/2 . . . . . solve the given relation for y

... f(x) = x·y = x(160 -x)/2 . . . . . substitute the expression for y into the product

... f'(x) = 80 -x = 0 . . . . . . . . . . find the derivative of f(x) and set it to zero

... x = 80 . . . . . . . . . . . . . . . . . add 80

... y = (160 -80)/2 = 40 . . . . . . find the value of y

The first number is 80.

The second number is 40.

answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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rauschg

rauschg · hand

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c

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it would be c