Please need question 1 and 2 solved thank you for yeur own Jearning Lab assignme

Question

Please need question 1 and 2 solved thank you for yeur own Jearning Lab assignments are alwaps due on the next Twesday, after they are assigomed SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem 1) From a thin piece of cardboard 10 in. by 10 in, square corners are cut out so that the sides 1) can be folded up to make a box. What dimensions will yield a box of maximum volume? What is the maximum volume? Round to the nearest tenth, if necessary 2) Suppose a business can sell x gadgets for p- 250-0.01x dollars apiece, and it costs the 2) business cfx) -1000 25x dollars to produce the x gadgets. Determine the production level and cost per gadget required to maximize

Explanation / Answer

1. Let x square inches cut off at each corners

So volume = x(10-2x)(10-2x)

V = 4x3 - 40x2+100x

V ' = 12x2-80x+100

V ' = 0

12x2-80x+100=0

x= 5/3 inches

And the length and width = 10 -2(5/3) = 20/3 inches

Volume = (10/3)(20/3)(20/3) = 148.15 inches3

2.Profit = Revenue - cost

P(x) = px - C(x)

P(x) = 250x -0.01x2-1000-25x = -0.01 x2+225x-1000

P'(x) = -0.02x +225

P '(x) = 0

-0.02 x + 225=0

x =11250

Cost per gadget, p=250-0.01(11250) = 137.50

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