Can you solve this math problem? Â

Can you solve this math problem?  

answers 0:An orthodontist uses two types of appliances (A and B), both shown to be effective for overbites. Over a year, each appliance A requires 6 hours of the doctor’s labour and 14 hours of the dental assistants’ labour; each appliance B requires 4 hours of the doctor’s labour and 16 hours of the dental assistants’ labour. Over the year the doctor cannot put more than 1200 hours of labour for appliances, and the assistants cannot put more than 3200 hours. Under these conditions the orthodontist makes a profit of $2000 on appliance A and $1500 on appliance B.(a)State the decision variables and construct the mathematical model for this linear programming problem by stating the objective function, the problem constraints and the non-negative constraints. (b)Using graphing techniques clearly ind! icate the feasible region by shading. (c)Find and label each corner point on your graph. (d)Determine how many of each type of appliance should the doctor use to maximize profits. (e)State the maximum profit? Thank you very much !...Show moreanswers 1:a) Let the dentist decides to use x nos. of appliance A and y nos.of appliance B Then optimize Profit (x,y) = 2000x 1500y, with following constraints6x 4y ≤ 1200 ; constraint for doctor's labour not more than 1200 hours, OR3x 2y ≤ 600 --------------1) 14x 16y ≤ 3200 ; constraint for assistant's labour not more than 3200 hours, OR7x 8y ≤ 1600 ------------2)x ≥ 0 ; constraint non negative use of Appliance Ay ≥ 0 ; constraint non negative use of Appliance BIf you plot all these lines in a graph and shade the left hand side of line you will find the extreme right corner is the solution which is intersection of two lines represented by eqn 1) and 2)b)..|..C |*.....|...* 3x ! 2y ≤ 600..A.|o....*.....|.....o..*.....|............o P....! .|..............*.....o 7x 8y ≤ 1600.... |_________*_____o___.....................B.........DShade area APB with dark color and other area with light color (to the left side of lines)c) Now solve for corner points and intersection point Pfor example for A, plug x = 0, in 7x 8y = 1600, you get y = 200, so A (0, 200)similarly B (200,0), C(0,300), D(228.57, 0) and d) P is intersection of two lines so solve them and you get P(160,60) which is your solutione) Now optimum solution will be when dentist uses 160 of A appliances and 60 of type B.Profit (160, 60) = $2000*160 $1500*60 = $410,000 ---------Answerto plot graph, put x = o to get y intercept and y = 0 to get x intercept, then connects the two points.Hope this helpedVick...