49 A volunteer wants to crochet beach hats and baby afghans

49) A volunteer wants to crochet beach hats and baby afghans for a church fund-raising bazaar 49) She needs 8 hours to make a hat and 3 hours to make an afghan and she has 24 hours available. Write an inequality that describes the situation and use the inequality to decide whether she can make 2 hats and 2 afghans in the time allowed. Let x represent the number of hats and y the number of afghans that she makes. A) 8x +3y 24; no C) 8x+3y s 24; no B) 8x+3y 24; yes D) 8x + 3y s 24; yes 50) A steel company produces two types of machine dies, part A and part a $2.00 profit on each part A that it produces and a $6.00 profit on each part B that it produces Letx - the number of part A produced in a week and y the number of part B produced in a week. Write the objective function that describes the total weekly profit. =2x + 6y C) z-6x+ 2y B) z -2(x -6)+ 6(y - 2) D)2=8(x + y) value of the given objective function of a linear programming problerm d the maximum or minimum value of the given objective function of a linear programming problem strates the graph of the feasible points. 51) Objective Function: z 2x + 4y Find maximum and minimum.

Solution

49. x is the number of hats and y is the number of afghans made by the volunteer. Since each hat takes 8 hours to make and since each afghan takes 3 hours to make, the time required to make x number of hats is 8x and the time required to make y number of afghans is 3y.Since the volunteer has 24 hours available, we have 8x + 3y 24. Thus, the answer D is correct. Further, to check whether the volunteer can make 2 hats and 2 afghans, let was substitute x = 2 and y = 2 in the inequality 8x + 3y 24 ;. Then 8*2 + 3*2 24 or, 16 + 6 24 24 or, 22 24 which is correct. Thus the volunteer can make 2 hats and 2 afghans in the time allowed.

50. x is the number of parts A produced and y is the number of parts B produced in a week. The profit on parts A produced @ $ 2 per unit is 2x per week and  profit on parts B produced @ $ 6 per unit is 6y per week. Thus, the total weekly profit z = 2x + 6y. The answer A is correct.

51.The feasible region of every linear programming problem is convex and the maximum or minimum is determined at one of the vertices of the feasible region. However, here, neither the constraints are stated and nor is the graph furnished. Therefore, the feasible region and therefore the vertices and the maximum/minimum cannot be determined.