Chapter 8 Case Study: Sew & Sew Inc. manufactures pants and vests. The revenue on each pair of pants is $65 and on each vest is $130. The pants use 1.5 yards of material and the vests use 2 yards of material each. Because of productions limitations, Sew & Sew can manufacture only 95 of these garments (vests and pants) per day, and can use only 175 yards of material per day. 1. If Sew & Sew can sell all the pants and vests it makes, find the number of each garment (vests and pants) it should produce per day. 2. Find the total revenue. (Must show your work, and explain each of your answer). Chapter 8 Case Study Help Please read the following sample: Thank you Here are the steps you need to follow: 1. Write down the Profit function: To do this: a. Let x be the number Ducks, and y the number of Geese, then the profit function is: P = 1.5x + 2y (1 point) b. Next, write the equation related to the cost of raising the birds: 1x + 1.5 y = 40 (2 points) c. Next, write the equation related to the number of birds he can raise: x + y = 30 (2 points) d. Solve for x, and y (3 points). e. State the profit (2 points) Hope this helps. Dr. P. Tran Answer to two of the following 5 questions: 1. Solve using any method: 2. Multiply the two matrices: 3. The total number of dimes and nickels is 50 coins, and their total value is 400 cents. Find the number of dimes and nickels. 4. Solve the system: x + y + z = 9 2x 5y + 3z = 1 3x + 2y 4z = 2 5. Solve the system: Answer 3: Let number of dimes is x and number of nickels is y . Since total number of coins is 50, set up first equation as x y 50 y 50 x Now Dime has worth 10 cents and Nickel has worth 5 cents. Since total value is 400 cents, set up second equation as 10 x 5 y 400 Using first equation, Substitute y 50 x in second equation and then solve for x 10 x 5 50 x 400 10 x 250 5 x 400 5 x 250 400 5 x 150 x 30 Plug in x 30 in first equation y 50 x and then evaluate y y 50 30 20 Therefore number of dimes is 30 and number of nickels is 20 . Answer 4: Consider the system of equation x yz 9 ...... 1 ...... 2 2 x 5 y 3z 1 ...... 3 3 x 2 y 4 z 2 Multiply equation 1 by 5 then add with equation 2 to obtain 5 x 5 y 5 z 45 2 x 5 y 3z 1 7 x 8 z 46 Label this equation as 4 ...... 4 7 x 8 z 46 Multiply equation 1 by 2 then add with equation 3 to obtain 2 x 2 y 2 z 18 3 x 2 y 4 z 2 x 6 z 20 Label this equation as 5 ...... 5 x 6 z 20 Multiply equation 5 by 7 then add with equation 4 to obtain 7 x 42 z 140 7 x 8 z 46 50 z 186 186 z 50 93 25 93 in equation 5 and then evaluate x 25 93 x 6 20 25 558 x 20 25 58 25 Plug in z 58 93 and z in equation 1 and then evaluate y 25 25 58 93 y 9 25 25 151 y 9 25 151 y 9 25 74 25 Plug in x 58 74 93 , , 25 25 25 Hence the solution is x, y, z Answer 3: Let number of dimes is x and number of nickels is y . Since total number of coins is 50, set up first equation as x y 50 y 50 x Now Dime has worth 10 cents and Nickel has worth 5 cents. Since total value is 400 cents, set up second equation as 10 x 5 y 400 Using first equation, Substitute y 50 x in second equation and then solve for x 10 x 5 50 x 400 10 x 250 5 x 400 5 x 250 400 5 x 150 x 30 Plug in x 30 in first equation y 50 x and then evaluate y y 50 30 20 Therefore number of dimes is 30 and number of nickels is 20 . Answer 4: Consider the system of equation x yz 9 ...... 1 2 x 5 y 3z 1 ...... 2 3x 2 y 4 z 2 ...... 3 Multiply equation 1 by 5 then add with equation 2 to obtain 5 x 5 y 5 z 45 2 x 5 y 3z 1 7 x 8 z 46 Label this equation as 4 7 x 8z 46 ...... 4 Multiply equation 1 by 2 then add with equation 3 to obtain 2 x 2 y 2 z 18 3x 2 y 4 z 2 x 6 z 20 Label this equation as 5 x 6 z 20 ...... 5 Multiply equation 5 by 7 then add with equation 4 to obtain 7 x 42 z 140 7 x 8 z 46 50 z 186 186 50 93 25 z 93 in equation 5 and then evaluate x 25 93 x 6 20 25 558 x 20 25 58 25 Plug in z 58 93 and z in equation 1 and then evaluate y 25 25 58 93 y 9 25 25 151 y 9 25 151 y 9 25 74 25 Plug in x 58 74 93 Hence the solution is x, y, z , , 25 25 25