Problem 2. A manufacturer has two products, A and B. Information on net returns
ID: 365412 • Letter: P
Question
Problem 2. A manufacturer has two products, A and B. Information on net returns for the products is given in the table below Product A Produdt B less than 100 100 to 200 more than 200 40 38 less than 30 31 to 50 more than 50 25 23 Each unit of A produced takes 3 hours of unskilled labor and 4 hours of skilled labor. Each unit of B produced takes 2 hours of unskilled labor and 1 hour of skilled labor. There are 1150 hours of unskilled labor, and 900 hours of skilled labor available to produce these items. There is a capacity limit of 600 items total at this plant a) Solve this problem via software using the "delta method." Interpret the output, including dual values AExplanation / Answer
As we are given that the two parts A and B are manufactured in the same plant using the same set of skilled and unskilled labour, the table denotes the values of different parameters like net returns – row 1, skilled labour-row 2 etc).
Column Max says le which stands for less than or equal to the RHS column. RHS column denotes what is th maximum number of labor hours (skilled=900 – row 2, unskilled=1150 – row 3, capacity limit of the plant = 600 – row 4 etc).
Next the column Used denotes the actual solution where the Objective - row 1 denotes the maximized value of the objective function (which should be to maximize revenues)
Row answer gives us the final optimal solution which denotes how many pieces of A and in which band (<100, 100-200, >200 etc) are to be produced. In this case it is 100,30 and 0 in each of the 3 bands. Similarly the quantities to be produced for product B in the 3 bands are 30,20 and 330 respectively.
Column used is the amount of skilled labour, unskilled labour usd to produce the above mentioned quantities of A and B. Eg – Total skilled labour used = 100*4+30*4+0*4+30*1+20*1+330*1 = 900
Similarly total unskilled labour= 100*3+30*3+0*3+30*2+20*2+330*2 = 1150
Total units produced = 100+30+0+30+20+330 = 510
Rows product A limit 1, product A limit 2, product B limit 1, product B limit 2 denote the number the solution row itself I.e 100,30,0,30,20,300 (I think product B limit 3 = 300 is missing)
Row total production is just the sum of products A (100+30=130) and B (30+20+330 = 380)
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