A manufacturer produces two models of toy airplanes. It takes the manufacturer 20 minutes to assemble model A and 10 minutes to package it. It takes the manufacturer 15 minutes to assemble model B and 12 minutes to package it. In a given week, the total available time for assembling is 1800 minutes, and the total available time for packaging is 1080 minutes. Model A earns a profit of $12 for each unit sold and model B earns a profit of $8 for each unit sold. Assuming the manufacturer is able to sell as many models as it makes, how many units of each model should be produced to maximize the profit for the given week?

Accepted Solution

Answer:A - 90 unitsB = 0 unitsStep-by-step explanation:Here we have two models A and B with the following particularsModel A B    (in minutes)   Assembly 20 15 Packing          10 12 Objective function to maxmize is the total profit[tex]z=12A+8B[/tex] where A and B denote the number of units produced by corresponding models.Constraints are[tex]20A+15B\leq 1800\\\\10A+12B\leq 1080[/tex]These equations would have solutions as positive onlyIntersection of these would be at the pointi) (A,B) = (60,40)Or if one model is made 0 then the points would beii) (A,B) = (90,0) oriii) (0, 90)Let us calculate Z for these three pointsA B Profit 60 40 1040 90 0 1080 0 90 720 So we find that optimum solution isA -90 units and B = 0 units.