Answer:
B) The company should have 8 production runs each year
Explanation:
Given :
Uniform annual demand, = 16000
Total cost, C = 500y + 2x
xy = 16000
[tex] x = \frac{16000}{y} [/tex]
Let's substitute [tex]\frac{16000}{y}[/tex] for x in C.
Therefore, we have :
[tex] C = 500y + 2( \frac{16000}{y} )[/tex]
[tex] C = 500y + \frac{32000}{y}[/tex]
In order to minimize the total storage and setup costs,
Differentiating wrt y:
[tex] C = C_m_i_n, \frac{dc}{dy}=0[/tex]
[tex] C'(y) = 500y + \frac{32000}{y^2} = 0 [/tex]
[tex] y^2 = \frac{320}{5} = 64 [/tex]
[tex] y = \sqrt{64} = 8 [/tex]
In order to minimize the total storage and setup costs, the company should have 8 production runs each year