Answer:
a) attached below
b) P( profit ) = TR(q) - TC(q) 
c) attached below
d) -$5000 ( loss ) 
Explanation:
Given data:
Fixed Cost = $10,000
Material cost per unit = $0.15
Labor cost per unit = $0.10
Revenue per unit = $0.65
<u>a) Influence diagram to calculate profit </u>
attached below 
<u>b) derive a mathematical model for calculating profit.</u>
VC = variable cost per unit , LC = per unit labor cost , MC = per unit marginal cost, TC = Total cost of manufacturing , FC = Fixed cost, q = quantity, TR = Total revenue, R = revenue per unit 
VC = LC + MC 
TC (q) = FC + ( VC * q )
TR (q) = R * q 
P( profit ) = TR(q) - TC(q) ------------ ( 1 ) 
c)  attached below
<u>d) If Cox Electrics makes 12,000 units of the new product </u>
The resulting profit = -$5000
q = 12 
P = TR ( q ) - TC ( q ) 
   = ( R * q ) - ( Fc + ( Vc * q ) )
   = ( 0.65 * 12000 ) - ( 10,000 + ( 0.25 * 12000 ) 
   = -$5200