Solve the following game for optimal strategy based =3 =9 d=9 e:l B₁ A₁ 9+ a
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- 2. Sid and Nancy are marketing managers for competing running shoe companies. They are comparing their annual profit equations in tems of the number of pairs of shoes manufactured and sold. Sid's equation is P= -6n² + 72n - 192. Nancy's equation is P = -8n? + 40n -32. In both equations, P is the profit, in thousands of dollars, and n is the number of pairs of shoes manufactured and sold, in thousands. a) Compare the companies in terms of maximum profit, the number of pairs of shoes manufactured to reach the maximum profit, and the break-even points (when each company's profit is zero dollars). b) Choose either Sid or Nancy's equation. Using vertex form, describe the transformations of their Profit equation.Last week at Chili's, my wife and I played a game on a tabletop video screen. The object is to move your frog so that it hits every lily pad exactly once. The frog cannot move diagonally, and cannot go back in the direction it came from. Lily pads disappear after the frog jumps off of them, and the frog can't jump over an existing lily pad. T 10 A winning path is 0-0-0-0-0-0-0-0-0-0-0. X Śif y=x4 +4x3 +10 then find y2 and y3
- EACHER One of the authors enjoys mixing his cereal, eating 2 cups of a combination of Cheerios and Kashi GOLEAN! Crunch each morning. Cheerios contain 3 grams of fiber per cup while Kashi GOLEAN! Crunch contains 8 grams of fiber per cup.t The author wants to eat 2 cups of cereal, consisting of a combination of Cheerios and Kashi, and wants his bowl of cereal to contain 12 grams of fiber. (a) What are the unknowns in this situation? O the number of cups of Cheerios the author should eat O the number of cups of Cheerios and the number of cups of Kashi the author should eat O the combined number of cups of Cheerios and Kashi the author should eat O the number of cups of Kashi the author should eat (b) Create a system of equations to model this situation. (Let c represent the number of cups of Cheerios the author eats and k the number of cups of Kashi he eats.) total amount of cereal grams of fiber acer3.) A local school is planning a field trip to see a play. They must pay $100 to the bus driver, and $7 for each ticket. The school ended up spending $443 total. Which equation represents the situation? How many tickets were purchased in all? A 7t+443=100;49 tickets B 7t+100=443; 49 tickets C 100t+7=443; 100 tickets D 7t-100=443; 78 tickets2.) The Aitken Skateboard Company makes custom skateboards. They have figured out that their profit can be modeled by the equation: P = -2b? + 14b – 20 where b is the number of skateboards produced (in thousands >so for example 1,000 skateboards would be plugged in as 1) and P is the company's profit (in hundreds of thousands of dollars). • How many skateboards should they produce to maximize their profit? What is their max profit? Explain how you found that value. • How many skateboards should they produce to make zero profit? (Known as the break even point). Explain how you found that value. What is the companies ' profit if they produce 3,000 skateboards? 4,500 skateboards? Explain how you found those values.
- Vic is buying mulch and fertilizer for his front yard. A bag of mulch costs $4, and a bag of fertilizer costs $18. He knows he will need to buy at least 4 bags of mulch and at least 2 bags of fertilizer. Altogether, Vic wants to spend less than $80. Suppose Vic buys x bags of mulch and y bags of fertilizer. Given the information above, which of the following are possible values for x and y?Find the solution. (D³ + 6D² + 11D + 6)y = 0 -2x Av=ce-tre-te +c -3x By=c₁e*+c₂ C +czxe © y = c₁₂e-²x + c₂e²x + c₂e² -2x -3x (D y = c₂₁x² + c₂e² + cze -3xVic is buying mulch and fertilizer for his front yard. A bag of mulch costs $4, and a bag of fertilizer costs $18. He knows he will need to buy at least 4 bags of mulch and at least 2 bags of fertilizer. Altogether, Vic wants to spend less than $80. Suppose Vic buys x bags of mulch and y bags of fertilizer. Given the information above, which of the following are possible values for x and y? Select all that apply.
- For which three numbers k does elimination break down? Which is fixed by a row exchange? In each case, is the number of solutions O or 1 or oo?kx + 3y = 63x + ky = -6.18. Bill and Felicia each bake cookies for a party. Bill bakes 3 times as many cookies as Felicia. Felicia bakes 24 fewer cookies than Bill. Bill bakes b cookies and Felicia bakes f cookies. What pair of equations can be used to determine the number of cookies Bill and Felicia bake? A. b = 3(f + 24) f = b – 24 B. b= 3f f = 24 – b C. b= 3f f = b – 24 D. f = 3b b =f – 241. The paths of two dolphins playing in the ocean were recorded by some biologists. The first dolphin's path could be modelled by the equation h(t) = 2t4 - 17t³+27t² 252t +232 and the second dolphin's path could be modelled by the equation h(t) = 20t³ - 20² +300t - 200. When was the first dolphin higher than the second dolphin?