A printer has a contract to print 100,000 invitations for a political candidate. He can run the invitations by using any number of metal printing plates from 1 to 20 on his press. For example, if he preparates 10 plates, each impression of his press makes 10 invitations. Preparing each plate costs $8 and he can make 1000 impressions per plate per hour. If it costs $ 128 per hour to run the press, how many metal printing plates should the printer use to minimize the cost of printing the 100,000 invitations?
A.- To undertand the problem:
1.- determine how many hours it would take to print the 100,000 invitations with 10 plates.
2.- How much would it cost to print the invitations with 10 plates?
3.- Determine how much it would cost to prepare 10 printing plates.
4.- What is the total cost to make the 10 plates and print the invitations?
B.- To find the number of plates that will minimize the total cost of printing the invitations:
1.- Find the cost of preparing x plates.
2.- Find the number of invitations that can be made with one impression made by x plates.
3.- Find the number of invitations that can be made per hour with x plates and the number of hours it would take to print 100,000 invitations.
4.- Write a function of x that gives the total cost of producing the invitations.
Neat and detailed solutions to all the parts of the question are provided.