Answer all multiple choice and give reasoning for every answer

Q1. Alice runs a restaurant and needs to purchase bananas and carrots to make her dishes. Suppose the price of bananas is P dollars per kg, the price of carrots is dollars per kg, and Alice can spend no more than )|/ dollars. Note: You should think of P, , and )[ as strictly positive parameters. A) Select the one correct statement from the following. O i. If Alice wants to purchase & kg of bananas and kg of carrots, then her expenditure willbe - + p - y dollars. O ii. If Alice wants to purchase x kg of bananas and kg of carrots, then her expenditure willbe p- 2 4+ - y dollars. O ii. If Alice wants to purchase 1 kg of bananas and 1 kg of carrots, then her expenditure will be P - dollars. O iv. If Alice wants to purchase kg of bananas and kg of carrots, then her expenditure will be p + dollars. B) If Alice chooses to buy only bananas, then what is the maximum quantity of bananas she can buy given that she can spend no more than M dollars? Oi. DZ O ii. O iii. O iv. M C) If Alice chooses to buy only carrots, then what is the maximum quantity of carrots she can buy given that she can spend no more than M dollars? Oi. M O ii. M O iii. O iv. a.7D) Suppose Alice buys x kg of bananas, where is no more than the maximum quantity of bananas that she can buy. For AT that she can buy? any such x, what is the maximum quantity of carrots - y Oiii. " =y=x Oiv. y"* =7 -2.2 E) The graph of f will be a straight line. What is the absolute value of the slope of this straight line? O i O i O iv. F) Which one of the following is the correct interpretation of the absolute value of the slope of f? O i O iii. O iv. If Alice wants to buy one more kg of carrots, then how many kg of bananas she will have to give up. If Alice wants to buy one more kg of carrots, then how many additional kg of bananas she can buy. If Alice wants to buy one more kg of bananas, then how many kg of carrots she will have to give up. If Alice wants to buy one more kg of bananas, then how many additional kg of carrots she can buy. G) Which one of the following provides the correct interpretation of the z-intercept and -intercept when you draw the straight-line graph of f? O i O iii. O iv. The intercept gives the minimum quantity of bananas that Alice can buy, and the intercept gives the minimum quantity of carrots she can buy. The x intercept gives the minimum quantity of bananas that Alice can buy, and the intercept gives the maximum quantity of carrots she can buy. The x intercept gives the maximum quantity of bananas that Alice can buy, and the intercept gives the minimum quantity of carrots she can buy. The x intercept gives the maximum quantity of bananas that Alice can buy, and the intercept gives the maximum quantity of carrots she can buy. H) Suppose p = 1, q = 2, and M = 100. Which one of the following is not a feasible purchasing-plan for Alice? O i. (0, 50) O ii. (20, 20) O iii. (0, 0) O iv. (40, 40) O v. (100, 0) O vi. (20, 40) O vii. (70, 0) O viii. (0, 20)() Suppose p = 1, q = 2, and M = 100. Which one of the following statements is correct about the purchasing-plan (40, 60). O i. This is a feasible purchasing-plan, and if Alice executes this purchasing-plan then she will utilize all the money she has. O ii. This is a feasible purchasing-plan, and if Alice executes this purchasing-plan then she will be left with 10 dollars out of the 100 dollars she has. O iii. This is an infeasible purchasing-plan, and if Alice wants to execute this purchasing-plan then she will somehow need to find an additional 60 dollars. O iv. This is an infeasible purchasing-plan, and if Alice wants to execute this purchasing-plan then she will somehow need to find an additional 40 dollars.J) If the purchasing plan , y is a feasible purchasing-plan, then it must be that Oi. p . x+q . yz M O ii. p . x+q . y MA) Find the two unknown numbers such that their sum is the number a and their difference is the number b. Note that the two unknown numbers you find -- a* and y* -- will be in terms of a and b. Oi. x* = 2-6 O ii. x* = 2to 2' y a-b 2 O iii. x* = atb y'y - ab O iv. x* = at 2 , y = atb 2 O v. x* = (a+ b), * = (a-b) B) Let s denote the sum of two unknown numbers, and d denote their difference. Find the two unknown numbers if we know that es = a and ed = b. Note: As discussed in class, the "e" mentioned above is the Euler's number (close to 2.71). The two unknown numbers you find -- x* and y* -- will be in terms of a and b. Oi. x* = In(va - b), y* = In(va +b) O ii. x* = In(Va +b), y* = In(Va-b) O iii. x* = In(Va . b), y* = In(VB) O iv. x* = In(V;). y* = In(va. b)C) Find the two unknown numbers -- X and y - such that both of the following 2 conditions are satisfied. Equation 1. 3 - 2 . erty _ 2 . e"-y = 0 Equation 2. 1 - 2 . erty + 2 . e"-y = 0 Oa. x* = In(V2), y* = In(V2) O b. a* = In(2), y* = -In(v2) O c. x* = -In(V2), y* = -In(v2) O d. x* = -In(V2), y* = In(v2)Q5) Suppose a missile is launched vertically upwards from ground-level at time () with an initial velocity of . The missile will start going up, but due to the force of gravity it's velocity will decline. The missile will reach a maximum height, and then start coming down towards the ground. Suppose the height of the missile (in meters) relative to ground-level { seconds after it is launched is given by the quadratic function: h(t) = - %gz'g > 0 Inequality 2. x2+ y - K . d O c. V100 + d - > . d O d. 100- A . d