Assignment:
Imelda manages a shoe factory that makes two types of shoes: casual shoes and dress shoes. The factory can make a total of 1,000 pairs of shoes per day. On any given day, it cannot make more than 800 casual pairs of shoes. Each pair of casual shoes needs 2 units of labor, while each pair of dress shoes needs 3 units of labor. The factory has 2,400 units of labor available daily. Each pair of casual shoes earns a profit of $15, while each pair of dress shoes earns a profit of $20. How many pairs of each type should the factory make each day?
(Through Simplex LP Solver model, the answers for the decision variables are 600 casual shoes and 400 dress shoes)
Assignment continues analyzing Imelda's shoe factory. To grow her business, in the long run, Imelda is considering two options:
Option A: She can hire 40 more units of labor daily at the cost of $4.50 per unit.
Option B: She can invest in technology and increase the daily total capacity by 50 pairs of shoes. This investment has a one-time cost of $50,000. Applying a straight line amortization schedule over one year (250 working days), Imelda finds the daily cost of this investment to be $200.
Which option is better?
Under Option A:
Net impact =
Change in production:
Under Option B:
Net impact =
Change in production:
Suppose labor costs $5 per unit and the new technology has to be amortized over 6 months. What should Imelda do?
Ignoring the questions above, use SolverTable to discuss the effects of extending labor on the Objective function, when each unit of additional daily labor costs $4.50. Include a well-formatted table as Exhibit A. What would be your recommendation to Imelda?
Ignore the questions above. Imelda does not want more than 40% of the produced shoes to be casual shoes. Write down this constraint, so that the resulting model is still linear.