- 4 Profit Decreases Over Intervals Where The Cost Of Producing An Extra Item Exceeds The Revenue Generated From Producin 1 (37.59 KiB) Viewed 65 times
- 4 Profit Decreases Over Intervals Where The Cost Of Producing An Extra Item Exceeds The Revenue Generated From Producin 2 (39.39 KiB) Viewed 65 times
- 4 Profit Decreases Over Intervals Where The Cost Of Producing An Extra Item Exceeds The Revenue Generated From Producin 3 (37.96 KiB) Viewed 65 times
- 4 Profit Decreases Over Intervals Where The Cost Of Producing An Extra Item Exceeds The Revenue Generated From Producin 4 (34.6 KiB) Viewed 65 times
- 4 Profit Decreases Over Intervals Where The Cost Of Producing An Extra Item Exceeds The Revenue Generated From Producin 5 (44.11 KiB) Viewed 65 times
5. Profit increases over intervals where the revenue generated from pro- ducing an extra item exceeds the cost of producing an extra item. Determine the open interval(s) (x-intervals) where marginal revenue ex- ceeds marginal cost. In CAS Perspective, type Solve (R'(x)>C'(x)). Write your answer (as an interval) below. Since a represents items pro- duced and sold, you can eliminate all negative values of a from consid- eration. For infinite intervals, just type inf or infinity to indicate the interval has no upper bound. R'(x) > C'(r) on the interval(s):_ On this interval(s), profit is creasing (increasing or de-
6. If profit is to be maximized, it occurs when the marginal cost equals marginal revenue. Determine the number of items produced and sold for which the marginal functions agree. In the CAS Perspective, type Solve(R'(x)=C'(x)). Write your answers below. Again, consider only x ≥ 0. C'(x) = R'(x) when z = items 7. Determine if your answer in #6 maximizes or minimizes profit by filling in all of the blanks below? Since C'(x)= R(x) when z = C'(x) > R'(a) on the interval interval profit is minized when = items, are produced and sold, and R'(x) > C'(x) on the (marimized or items are produced and sold.
8. Now let's confirm our results using the profit function. In the CAS Perspective, type P(x):=R(x)-C(x). This is the profit function. Write it below as it appears in the CAS panel, with like terms collected. P(x) = 9. In the CAS Perspective find the marginal profit function by typing P'(x) or Derivative(P(x)). Write your answer below as it appears in the CAS panel. MP(x) = P'(x) =_ 10
10. Recall that local extreme values of a function can occur only at the crit- ical numbers of the function (domain values at which the derivative is equal to zero). Find the positive critical numbers of P(x) by typing Solve(P'(x)=0) in the CAS Perspective. Write your answer(s) in the space provided. Explain how these answers relate to your work with the marginal functions. Recall we are only considering x ≥ 0. Critical Number(s) of P(x): x= Type a sentence or two explaining how your answer here relates to your answers above with the marginal functions. Look at your answer for #6. items