Math 11 Scimmage Test 1 1.) The variable cost to manufacture an item is $10 , and it costs $2, 500 to produce 100 items. Write the cost function, then use it to estimate the cost of manufacturing 300 items. 2.) A firm producing video tapes has fixed costs of $6, 800 , and a variable cost of 30cents per tape. If the video tapes sell for $2 each, find the number of tapes that must be produced to break-even. 3.) A person takes three daily vitamin supplements, B, C, and E, via three types of pills, regular, extra strength, and fortified. Each regular pill contains 10 units of B, 20 units of C, and 20 units of E. Each extra strength pill contains 20 units of B, 60 units of C, and 10 units of E. Each fortified pill contains 10 units of B, 20 units of C, and 40 units of E. How many pills of each type should be taken in order to achieve 50 units of B, 120 units of C, and 90 units of E? Set up the sytem of equations, and write the augmented matrix for the system. 4.) Let A(0,2) and B(3,0). Find the equation of the line through A perpendicular to the line containing A and B. 5.) A firm produces a machine for $50,000 and the machine has a useful life (determine by tax laws) of ten years. If the machine depreciates $4,000 per year, find: a.) The value of the machine, V, after t years. b.) Find V(10), the salvage value of the machine. 6.) A travel Agency is planning charter flights to Hawaii for exactly 1400 passengers aboard two types of jets. Each 747 jet holds 400 passages and each 707 holds 150 passengers. The rental fee is $15,000 for each 747 and $9,000 for each 707. If exactly $66,000 must be used for renting the jets, how many of each type should be ordered? 7.) A woman wants to use milk and orange juice to increase the amount of calcium and vitamin A in her daily diet. An ounce of milk contains 37milligrams( mg ) of calcium and 57micrograms( g ) of vitamin A. An ounce of orange juice contains 5mg of calcium and 65g of vitamin A. How many ounces of milk and orange juice should the woman drink each day to provide exactly 500mg of calcium and 1, 200g of vitamin A? Set up the sytem of equations, and write the augmented matrix for the system. 8.) A shoe company makes special shoes for runners, hikers, and bikers on three different machines. Each running shoe requires 1 hour on each machine; each hiking shoe requires 2 hours on machine A, 1 hour on machine B, and 2 hours on machine C; each biking shoe requires 2 hours on machine A, 1 hour on machine B, and 1 hour on machine C. Machine A is available exactly 26 hours a week, machine B 21 hours a week, and machine C 23 hours a week. How many shoes of each type can be made each week? 9.) The sum of the digits of a two-digit number is 14. If the digits are reversed, the value of the number is decreased by 18. Find the number. (Use system of equations) [Hint: if xy is two-digit number, then the value of xy is 10x + y ] 1 10.) Write the system of equations for the following matrix equations: a.) 11.) 1 3 6 x + y = 2 4 5 b.) 2 2 0 p 1 0 2 2 r = 2 2 0 2 t 3 If A and B are invertible matrices then ( AB) = B 1 A 1 . 5 2 3 1 1 1 Let A 1 = , and B = 7 3 . Find ( AB) and AB. 3 1 1 a b -1 Note: if A = , then A = c d 12.) Solve: d ad - bc -c ad - bc -b ad - bc a ad - bc 3x - 5y = 2 . Use X = A-1B, where A-1 = -x + 2y = 0 2 5 1 3 1 0 1 2 13.) Write the system of equations and find the solution, X, if aug ( A ) = 0 1 2 3 0 0 1 4 2