In Exercises 1–4, determine whether the given point is in the feasible set of the furniture manufacturing problem. The inequalities are as follows.
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- 2. Show that the feasible set constrained by the inequalities x > 0, y > 0, 2x+5y < 3, –3x+8y < -5 is empty.arrow_forwardWhich points are IN the feasible region of the following system of inequalities? Select all that apply. HINT: graphing is not needed to answer this question. 2x+y ≤ 10 x+2y ≤8 x>0 y20 (6.-3) (3.1) (2.5) (1, 2) (0.5.3)arrow_forwardIn Problems 45–49, solve each inequality. Graph the solution set.arrow_forward
- 2. Maximize z = 2x₁ + x₂ subject to: x1 + x₂ ≤7 2x₁11 2x2 ≤7 X1, X20 ₁ and ₂ integersarrow_forwardQ2) Solve the following LP problem by graph: Maximize P = -x + 5y (x-2y 20 y ≤100 Subject to x + y 210 x ≥0, y≥0arrow_forwardSolve. Maximize P = 4x + 3y, subject to:3x + 5y ≥ 203x + y ≤ 16– 2x + y ≤ 1x ≥ 0, y ≥ 0arrow_forward
- 3. Jack and Jill work at the same store. Jack's total weekly salary, in dollars, if he sells x items is given by S= = 100 + 5x, and Jill's total weekly salary, in dollars, if she sells x items is given by S = 80 + 6x. If they sell the same number of items in a week, what is the minimum number of items they have to sell so that Jill's weekly salary is at least $300 more than Jack's? Verarrow_forward1.) A retiree has 60 garden plots on which he could plant cabbage and pechay. His friend told him that he could make a profit of Php 100 per slot of cabbage and Php 90 per slot of pechay. His household could not possibly take care of more than20 plots of cabbage and 40 plots of pechay. How many plots of each vegetable should he plant for him to have a maximum profit? What is the maximum profit? 2.) A chemist makes a component of orchid fertilizer that requires two secret ingredients labeled as A and B. She sells ingredient A at Php 200 per kilogram and ingredient B at Php 350 per kilogram. Per production, a kilogram of ingredient A requires 4 units of special pollen while 3 units for each kilogram of ingredient B. Suppose the excess of ingredient B over ingredient A per production should be at most 4 units, and there are only 24 units of special pollen available per production, how many kilograms of ingredient A and ingredient B should be made per production to maximize the sales?arrow_forwardMaximize P=2x1−3x2+4x3, Subject to: 4x1−3x2+x3 ≤3 x1+x2+x3 ≤10 x1,x2,x3 ≥0arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageGlencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill