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Differential Calculus in Derivative Rules, show the solution every number and answers.
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- Eliminate the arbitrary constants of: x^2=Axy+ByA fertilizer producer finds that it can sell its product at a price of p = 300 − 0.1x dollars per unit when it produces x units of fertilizer. The total production cost (in dollars) for x units is C(x) = 15000 − 125x + 0.025x 2 . If the production capacity of the firm is at most 1000 units of fertilizer in a specified time, how many units must be manufactured and sold in that time to maximize the profit?-3x+y=-17 -x+y=-5 substitution method.
- Maximize Z = 10x1 + 20x2; Subject to -x1 + 2x2 ≤ 15 x1 + x2 ≤ 12 5x1 + 3x2 ≤ 45 and x1 ≥0, x2 ≥ 0A company manufactures two types of bicycles, a racing bicycle and a mountain bicycle. The total revenue (in thousands of dollars) from x1 units of racing bicycles and x2 units of mountain bicycles is R = −6x21 − 10x22 − 2x1x2 + 32x1 + 84x2 where x1 and x2 are in thousands of units. Find x1 and x2 so as to maximize the revenueMax Z = 6XI + 4X2 Subject to 7XI + 8 X2 ≤224 8XI + 12 X2 ≤192 15XI + 16X2 ≤480 Xi ≥ 0
- A company manufactures two types of sneakers: running shoes and basketball shoes. The total revenue from x1 units of running shoes and x2 units of basketball shoes is: R=-5x1 2-8x2 2-2x1x2+50x1+97x2 where x1 and x2 are in thousands of units. Find x1 and x2 so as to maximize the revenue.What if we have x(0)=[3, -3] and x_1'(t)=19x_1(t) - 10x_2(t), x_2'(t)=30x_1(t) - 16x_2(t) what would be the solution then?A financier plans to invest up to $500,000 in two projects. Project A yields a return of 8% on the investment of x dollars, whereas Project B yields a return of 15% on the investment of y dollars. Because the investment in Project B is riskier than the investment in Project A, she has decided that the investment in Project B should not exceed 40% of the total investment. How much should the financier invest in each project in order to maximize the return on her investment?
- A company wants to increase the 10% peroxide content of its product by adding pure peroxide (100% peroxide). If x liters of pure peroxide are added to 500 liters of its 10% solution, the concentration, C, of the new mixture is given by : C = [x + 0.1(500)] / (x + 500). Then solve: How many liters of pure peroxide should be added to produce a new product that is 28% peroxide?.A company wants to increase the 10% peroxide content of its product by adding pure peroxide. If x liters of pure peroxide are added to 500 liters of its 10% solution, the concentration, C, of the new mixture is given byHow many liters of pure peroxide should be added to produce a new product that is 28% peroxide?On the basis of projections for the year 2022, the number of women and men in the workforce (in millions) can be estimeted by Women: -7x+16y=1070 Men: -5x+10y=759 where x=14 correspondds to the year 2014. According to these models, will the number of women in the workforce equal the number of men during the time period from 2014 to 2022 (that is, 14 ≤ x ≤22)?