IGNOU MTE 14 2026 - Consider the cubic total cost function Assume tha

Question

Consider the cubic total cost function

$$C = 0.06q^3 - 0.8q^2 + 13q + 10$

Assume that the price of q is 15 per unit. Find the output which yields maximum profit.
b) Apply dominance to find the optimum strategies of A and B from the pay-off matrix given below

	Player B
		u	v
	x	`6(2)`	`7(3)`
Player A	y	`4(7)`	`9(3)`
	z	`7(1)`	`8(2)`

c) Suppose that the previous forecast was 2090 and the actual value of the variable of interest for the period was 1985 and the oldest value of interest was 1955. Using the moving average technique based upon the most recent four observations find new forecast for the next period.

09 Jan 2026

Answer :

Word Count : 290

The total revenue is (R = 15q). Hence profit is (\pi = R - C = 15q - (0.06q^{3} - 0.8q^{2} + 13q + 10) = -0.06q^{3} + 0.8q^{2} + 2q - 10). For maximum profit, (\dfrac{d\pi}{dq} = -0.18q^{2} + 1.6q + 2 = 0). Multiplying by 100 gives ( -18q^{2} + 160q + 200 = 0), or (18q^{2} - 160q - 200 = 0). Dividing by 2, (9q^{2} - 80q - 100 = 0). Solving, (q = \dfrac{80 \pm \sqrt{80^{2} + 4 \cdot 9 \cdot 100}}{18} = \dfrac{80 \pm \sqrt{10000}}{18} = \dfrac{80 \pm 100}{18}). The feasible root is (q = \dfrac{180}{18} = 10). Thus maximum profit

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