Question

4. You manage a crew of 160 workers who could be assigned to make either of two products. Product A requires two workers per unit of output. Product B requires four workers per unit of output. a) Write an equation to express the combinations of products A and B that could be produced using exactly 160 workers. b) Measuring the quantity of product A on the horizontal axis and the quantity of product B on the vertical axis, use vertical lines to hatch the area depicting the combinations of A and B that could be produced with 160 workers (assume that it is also possible for workers to do nothing at all). c) Suppose now that every unit of product A that is produced requires the use of four shovels as well as two workers and that every unit of product B produced requires two shovels and four workers. Assuming that there are enough workers so that labor supply is not an issue, write down an equation describing the combinations of A and B that could be produced with exactly 180 shovels. In the graph from part b), use horizontal lines to hatch the area depicting combinations that could be produced with 180 shovels (assume that shovels can be left idle). d) In your diagram, locate the feasible combination of A and B that uses all of the labor and all of the shovels. Using your two equations for your input supply, confirm your answer algebraically. e) If you have 160 workers and 180 shovels, what is the largest amount of product A that you could produce? If you were to produce this amount, you will end up not using your entire supply of one of the inputs. Which one? How many units will be left unused?

Answer 1

a) Product A requires 2 workers while Product B requires 4 workers

Total number of workers=160

So,the equation which express the combinations of products Aand B that could be produced using exactly 160 workers can be written as : 2A + 4B = 160

b) see the attached diagram

c)Now, if every unit of product A requires the use of 4 shovels as well as 2 workers and that of product B requires 2 shovels and 4 workers.The area on the graph is shaded by a pencil to depict the area which is the combinations of A and B that could be produced with 180 shovels if there were no worries about the labour supply.

The equation for the combination which requires 180 shovels is as follows: 4A + 2B= 180

The black shaded area depicts the output combination when one takes into account both the limited supply of labour and shovels.

d)The two equations for the input supply are:

2A + 4B =160 and 4A + 2B =180

e)The largest amount of Product A that can be produced with 160 workers and 180 shovels is 45 units

The entire supply of one of the inputs which will not be issued here will be Workers.

The units left unused will be 70