Problem 5: Draw a constraint graph for the following set of inequalities. Use the Floyed- Warshall algorithm to find if this set of inequalities has a solution. Give a solution if it exists. x1-x3-1 x1 x2 <3 x3 x1 ≤1 x3-x2≤2
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- Plant A can produce 5 sedans and 4 minivans per week. Plant B can produce 10 sedans and 6 minivans per week. How many weeks should each plant operate to produce at least 40 sedans? Express your answer as a linear inequality with appropriate non-negative restrictions and draw its graph. Let x be the number of weeks that plant A is producing vehicles and let y be the number of weeks that plant B is producing vehicles. Ay 24 20 Choose the correct inequality with appropriate non-negative restrictions. O 5x+10y s 40, x20, y20 O 5x+10y 2 40, x20, y 20 O 5x+10y 40, x20, y20 16 12- Question Viewer Use the graphing tool to graph the inequality and the boundary lines representing the nonnegative constraints. Click to enlarge graph 12 16 20 Click the graph, choose a tool in the palette and follow the instructions to create your graph. Type here to search 99. n %23 立Use the graphing tool to graph in equality and the boundary lines representing the nonnegative constraints.Plant A can produce 4 sedans and 6 minivans per week. Plant B can produce 5 sedans and 3 minivans per week. How many weeks should each plant operate to produce at least 40 sedans? Express your answer as a linear inequality with appropriate non-negative restrictions and draw its graph. Let x be the number of weeks that plant A is producing vehicles and let y be the number of weeks that plant B is producing vehicles. Ay 24- 20- Choose the correct inequality with appropriate non-negative restrictions. 16- O 4x+5y > 40, x20, y 20 O4x+5ys 40, x20, y 20 12 4x + 5y < 40, x20, y 20 4x + 5y 2 40, x20, y 20 Use the graphing tool to graph the inequality and the boundary lines representing the nonnegative constraints. Click to 12 16 20 24 enlarge graph Click the graph, choose a tool in the palette and follow the instructions to create your graph. P Type here to search %23 立 O O
- A candidate has budgeted $9,900 to spend on radio and television advertising. A radio ad costs $495 per 30-second spot and a television ad costs $900 per 30-second spot. How many radio and television spots can the candidate purchase without exceeding the budget? Express your answer as a linear inequality with appropriate nonnegative restrictions and draw its graph. Let x be the number of radio spots and let y be the number of television spots. Choose the correct answer below and graph the inequality. A. 495x+900y≤9,900, x≥0,y≥0 B. 495x+900y<9,900, x≥0,y≥0 C. 495x+900y≥9,900, x≥0,y≥0 D. 495x+900y>9,900, x≥0,y≥0b. From part a, the inequality to determine the number of bags Ryan can place on the shelf is 5x+33≤80 where x denotes the number of 5-pound bags of flour. Consider 5x+33≤80 ⇒5x≤80-33 ⇒5x≤47 ⇒x≤475 ⇒x≤9.4. The constraints that are needed is x∈ℕ as the number of bags cannot be in fraction or is negative terms. Thus, x=9 as 9 is the largest natural number satisfying x≤9.4. Hence, Ryan can place 9 boxes on the shelf. The question: COMMUNICATE PRECISELY Is the answer to part b reasonable in the context of the situation? Explain your reasoning.1. Cullin needs to save at least P 1000 for homecoming. He works 2 jobs, earning P100/hour as waiter and P120/hour as mower. He only has 14 hours to work before the event. Which system of inequalities below correctly models his constraints? a. x + y ≥ 120 and x + y ≤ 100 b. 1000x + 120y ≤ 1000 and 2x + 100y ≤ 14 c. x + y ≥ 1000 and 100x + 120y ≤ 14 d. 100x + 120y ≥ 1000 and x + y ≤ 14 2. Inequality symbols used when its graph shows a solid line? 3. Jill and Jack want to improve their yards by planting lilies and roses. A pot of lily costs P 200 and a pot of rose costs P250. They should not spend more than P1500 for at least 7 plants. What is the system representing the possible number of pots of lilies (x) and roses (y) that could be sold to meet these conditions? * a. 200x + 250y ≥ 1500 and x + y ≥ 7 b. 200x + 250y ≤ 1500 and x + y ≥ 7 c. 200x + 250y ≤ 1500 and x + y ≤ 7 d. 200x + 250y ≥ 1500 and x + y ≤ 7
- Write the constraint below as a linear inequality. A canoe requires 3 hours of fabrication and a rowboat 5 hours. The fabrication department has at most 112 hours of labor available each week. Let x be the number of canoes and let y be the number of rowboats. Choose the inequality that represents the given constraint. A. 3x+5y2112 B. 5x + 3y ≤ 112 C. 5x+3y2112 D. 3x+ 5y ≤ 112Qn.2: A firm operates two types of machines A and B as shown in the table. Floor Space Available (M²) Number of Workers Type A 3 5 Type B 2 3 Maximum Space Available 18 30 The ratio of machines of type A to those of type B should be greater than one. Tasks a) Define the term linear programming | b) Write down four inequalities to represent the information above c) If the profit from using type A machine is Shs 6000 per hour and that of B is Shs 9000 per hour, write down the expression for the profit P in terms of x and y d) Find the number of machines of each type that should be in operation to give the maximum profit. Hence find the maximum profit e) What advice do you give to this company's managern order to maintain the weight and health of rabbits that will be sold for pets, rabbits must be fed a daily diet containing a minimum of 12 grams (g) of fat, 24 grams (g) of carbohydrates, and 5 grams (g) of protein and should be fed no more than eight ounces of food a day. What linear inequality, in terms of x and y, would represent the total amount of food in ounces?
- Write the constraint below as a linear inequality. A candidate will spend no more than $7800 on radio and TV advertising: Each radio spot costs $140 and each TV ad costs $790. Let x be the number of radio spots and let y be the number of TV ads. O A. 140x +790y s7800 O B. 790x +140y s 7800 OC. 790x + 140y z 7800 O D. 140x + 790y z 78003. Graph the inequality: 2 (x-1)2. Label the vertex. Test one set of coordinates that satisfies and does not satisfy the inequality. 3 5 4 -5 -4 -3 -2 -1 SP 2 1 حب -2 -3 -4 1 god 2 3 4 5 6Suppose that a MAX problem contained the following constraint: 5x + 9y ≤ 40. Then which of the following statements is true? 1.For the point (8, 5), the slack for this constraint would have a value of 45. 2.For the point (4, 2.5), the slack for this constraint would be a positive value. 3.For the point (4, 2), the slack for this constraint would be zero. 4.For the point (1, 4), the slack for this constraint would have a value of -1.
