A budget analyst has been asked to estimate total costs for

A budget analyst has been asked to estimate total costs for a new controller system for the DAX30 line of automation systems. Since this is a new product, there is no historical data to reference. However, the budget analyst estimates the following total cost function based on detailed information provided by the Production and Accounting Department personnel:

TC = $170,000 + $75Q + $0.0625Q² + $0.00125Q³,

where TC is Total Cost and Q represent the units of Output produced.

Part a – Determine the Variable Cost estimates of producing output levels between 0 and 500 units in 100 unit increments

Part b – Calculate the estimated marginal cost per unit relationship

Solution

Given that TC= $170,000 + $75Q + $0.0625 Q^2 + $ 0.00125 Q^3

a) The variable cost of the above production function is :

TVC= $75Q + $0.0625 Q^2 + $ 0.00125 Q^3

TVC (Q=100) = 7500+ 0.062544*10000 + 0.00125 * 100*100 * 100 = 7500+ 625.44 + 1250 = 9375.44

Similarly for Q=200, 300, 400 and 500, we have TVC = $27500, $61875, $120000 and $209375 respectively.

b) MC for the above relation is given by: 75+0.0625*2 + 0.00125*3 q^2 = 75.125 + 0.00125 Q^2

(Ans)