Question

Systems Engineering with Economics, Probability, and Statistics: Second Edition - Por C. Jotin Khisty, Jamshid Mohammadi, Adjo A. Amedkudzi.

Chapter 2 of the book - Exercise 24

24. A concrete-mix plant needs to hire a few men at either $5/hr (if semiskilled) or $3.50/hr (if nonskilled). The following data are available for making a decision:

Number of workers 2 3 4 5 6 7 8

Hours of output (yd³) 56 120 180 200 210 218 224

Additional fixed costs are $50/hr when ¡¡emiskilled labor is used and $60/hr wben nonskilled labor is used. Determine the number of workers to be hired to minimi.ze production costs. What is the corresponding cost per cubic yard?

Answer 1

because we need to minimise production costs, we first need to form the production cost function.

we will have two separate production cost functions for semi skilled and non skilled workers.

the production function for the semiskilled workers will be given as 50+5x where x is the number of hours and the production function for non skilled workers will be given as 60+3.5y where y is the number of hours. the combined production function will be

C= 110+5x+3.5y

differenciating partially wrt x and y gives us the values of x and y and consequently the min cost. for the number of workers and additional relation bw no. of hours and workers is required.