You manage a crew of 160 workers who could be assigned to make either of two products.

Question:

You manage a crew of 160 workers who could be assigned to make either of two products. Product A requires 2 workers per unit of output. Product B requires 4 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. ______. On the diagram below, use blue ink to shade in the area depicting the combinations of A and B that could be produced with 160 workers. (Assume that it is also possible for some workers to do nothing at all.)

(b) Suppose now that every unit of product A that is produced requires the use of 4 shovels as well as 2 workers and that every unit of product B produced requires 2 shovels and 4 workers. On the graph you have just drawn, use red ink to shade in the area depicting combinations of A and B that could be produced with 180 shovels if there were no worries about the labor supply. Write down an equation for the set of combinations of A and B that require exactly 180 shovels.
(c) On the same diagram, use black ink to shade the area that represents possible output combinations when one takes into account both the limited supply of labor and the limited supply of shovels.
(d) On your diagram locate the feasible combination of inputs that use up all of the labor and all of the shovels. If you didn€™t have the graph, what equations would you solve to determine this point?
(e) If you have 160 workers and 180 shovels, what is the largest amount of product A that you could produce? ______. If you produce this amount, you will not use your entire supply of one of the inputs. Which one? ______. How many will be left unused? ______.