Problem with productions - urgently!
since I am in high school and I am having an exam to university tomorrow, I hope you could help me quickly. The problem is that I do not know how to solve problems like that:
1) A business is currently selling 1000 novelty wind chimes for $100 each. It is estimated that for each decrease in price of $20, the monthly sales will increase by 200 chimes.
a) Find the demand function, p(x), where p is measured in dollars and x is the number of chimes sold. (I know how to solve this point)
b) Suppose a company is increasing the production of chimes by 15 chimes per month. Find the rate at which revenue is changing with respect to time when production is at 500 chimes. Include units. (This one - I do not :) )
I learnt that marginal costs/profit is estimated with the derivative of the cost/profit function, but I still have some questions. For instance, this one:
2) A company sells “student enhancement” products. The cost of producing x units of “enhancement” products is modeled by the function
C(x) = 400 + 50x +0.03x^2
a) Find the average cost function.
b) Find the average cost at a 100 units
c) Find the marginal cost at a 100 units and the marginal average cost at a 100 units.
d) Estimate the cost increase or decrease between producing 100 and 102 units.
I am desperately looking forward to your answers!