Greenfield Industries produces rotors for manufacturers in Hartford, Connecticut, and Des Moines, Iowa. Hartford needs at least 21 rotors, and Des Moines needs at least 40 rotors. Greenfield is able to produce and send at most 150 rotors to these two manufacturers. It cost $40 per rotor to ship to Hartford, and $50 per rotor to ship to Des Moines. In return for the purchases, Hartford gives Greenfield $20 in credits toward its products for each rotor purchased. Des Moines gives $15 in credits toward its products for each rotor purchased. Since Greenfield purchases a lot of materials from both companies, they have determined a need for at least $1,500 in credits.
How many rotors should be shipped to Hartford and Des Moines to minimize shipping costs? What is the minimum cost?
a. Let x represent the number of rotors shipped to Hartford and y represent the number of rotors shipped to Des Moines. Set up the cost objective function.
b. Write the Hartford constraint inequality for the number of rotors needed.
c. Write the Des Moines constraint inequality for the number of rotors needed.
d. Write the constraint inequality for the total number of rotors Greenfield is able to ship to these two locations.
e. Write the constraint inequality for the credits.
f. Graph the feasible region.
g. Identify the vertices.
h. What values will minimize cost in the objective function?