?no1.The demand function of a manufactures production is P=1000-2q where P is the price (per unit) when Q units

are demanded (per week) by consumers. Find the marginal revenue when 250 units are produced.?no2 The sum of $3000 is placed in the savings account. If money worth 6% compounded semi annually, what is
he balance in the account after 7 year? Assume no other deposit and no withdrawals are made

To find the marginal revenue when 250 units are produced, we need to find the derivative of the demand function with respect to q.

1. The demand function is given as P = 1000 - 2q, where P is the price per unit and q is the quantity demanded per week.

To find the marginal revenue, we need to calculate:
MR = d(TR) / d(q)

where TR represents total revenue.

Total revenue can be calculated as the product of price and quantity: TR = P * q.

Let's differentiate the total revenue function with respect to q:

d(TR) / d(q) = d(P * q) / d(q)

Now, substitute the demand function P = 1000 - 2q into the equation:

d(TR) / d(q) = d((1000 - 2q) * q) / d(q)

Expand and differentiate the equation further:

MR = d(1000q - 2q^2) / d(q)

MR = 1000 - 4q

Now, substitute q = 250 into the equation to find the marginal revenue when 250 units are produced:

MR = 1000 - 4(250)
MR = 1000 - 1000
MR = 0

Therefore, the marginal revenue when 250 units are produced is 0.

2. To calculate the balance in the savings account after 7 years with interest compounded semi-annually at a rate of 6%:

The formula for compound interest is: A = P(1 + r/n)^(nt)

A is the balance after time t, P is the principal amount (initial deposit), r is the annual interest rate (in decimal form), n is the number of times interest is compounded per year, and t is the number of years.

In this case, P is $3000, r is 6% (or 0.06), n is 2 (semi-annual compounding), and t is 7 years.

Substituting these values into the formula:

A = 3000(1 + 0.06/2)^(2*7)

Calculate the exponent first:

A = 3000(1 + 0.03)^(14)

A = 3000(1.03)^(14)

Now, calculate the value inside the parentheses (1.03) raised to the power of 14:

A = 3000(1.488737)

A ≈ $4466.21

Therefore, the balance in the savings account after 7 years with a 6% annual interest rate compounded semi-annually will be approximately $4466.21.