A photographer shoots at least 25,000 images in any given year. To do so, he considers leasing a combination of three cameras. The cameras he considers are large format, medium format, and compact format, one camera each. The leasing costs are $5,500, $2,100, & $700 for the three cameras regardless of how many images are taken with them, plus an additional 25, 12, & 5 per image taken with the respective cameras. The company that leases the cameras has put a limit of 10,000, 28,000, & 15,000 images that can be taken with the respective cameras. The photographer stipulates that at least 40% of the images that are actually taken will have to be taken with the large-format or the compact camera. (

a) Given that the photographer wants to determine which cameras to lease & how many images to take with the three respective cameras, formulate an optimization model that minimizes the photographer's total leasing costs.

(b) Formulate: If the large-format camera is leased, then the medium format camera must also be leased.

(c) Lease exactly two of the three cameras.

(d) If the large-format camera is leased and the medium -format camera is not leased, then the compact camera cannot be leased.

DEFINE ALL VARIABLES CAREFULLY. DO NOT SOLVE.