Response to the following problem:
Charley Judd is a salesman for Futura Farm Foods, which is currently marketing a feed for dairy cattle called Moo Town Buffet. On a recent visit to Norfolk, Nebraska, Charley called on Dan Preston, a successful dairy farmer with a herd of 100 dairy cattle.
Dan's success is due in part to a rigid diet he feeds his cattle. In particular, each cow receives a daily minimum of 100 units of calcium, 20,000 calories, and 1500 units of protein. To accomplish this regimen, Dan has been giving his cattle Cow Chow Feed. Each ounce costs $0,015 and supplies 1 unit of calcium, 400 calories, and 20 units of protein. In contrast, each ounce of the Moo Town Buffet Feed would cost Dan $0,020 and supply 2 units of calcium, 250 calories, and 20 units of protein.
a. How much is Dan Preston currently spending to feed a dairy cow each day using Cow Chow?
b. Why would Charley Judd not be successful in persuading Dan Preston to abandon his use of Cow Chow and switch exclusively to Moo Town Buffet?
c. Charley is a resourceful salesman, and he has offered Dan a plan to mix Cow Chow and Moo Town Buffet. The result would be a lower overall cost to Dan for a feed mixture that meets the minimum calcium, calorie, and protein requirements, and a sale for Charley.
What overall mix should Charley recommend to minimize Dan's overall feeding cost per cow? How much would Dan Preston save daily by feeding his 100 cattle the mixture recommended by Charley Judd?