The total cost of producing M units of a product, the optimal number of units in each batch is given by

where ƒ is the fixed setup cost to manufacture the product and k is the cost of storing one unit of the product for one year. 

(a) InkWe’R produces 40,000 gallons a year of laser toner. It costs $32 to set up their factory to produce a batch, and it costs $4 a year to store a gallon of toner. Find the number of gallons that should be produced in each batch to minimize the total production cost.
(b) Find and interpret q_ƒ(32, 40,000, 4).
(c) Find and interpret q_k(32, 40,000, 4).

Transcribed Image Text:

q(f, M, k) 2fM k