Question

A particular computing company finds that its weekly profit, in dollars, from the production and sale of x laptop computers is P(x) = -0.003x -0.2x + 600x - 800 Currently the company builds and sells 8 laptops weekly a) What is the current weekly profit? b) How much profit would be lost if production and sales dropped to 7 laptops weekly? c) What is the marginal profit when x = 8? d) Use the answer from part (a) and (c) to estimate the profit resulting from the production and sale of 9 laptops weekly a) The current weekly profit is $ (Round to the nearest cent as needed.)

Answer 1

- 800 Given p(x)= -0.003 x² – 0.2x² + 6002 - 800 al current & laptops will sell. So current profit is given by PC 8). So P18)= -0.00 3 853–0-208)2 +600(8) -800 P18) = 3,985-664 o so current weekly profit is 8 3925-66 Lowe b). SO NOW PUT)=-0.00341)?0.20112760017) | P(0)= 3,389.1711=3,389.17 so doop in profit is given by P18)- P(1) = 3985-66 -3,389.17 = 596.49. so drop in profit = 8 596.49 ] a so Now we know that profi formula for marginal profit function is given by plcx)= a(PID) V 6-0.003 x² _ 0.22² 4.6008_800). -0.003132?) – 0.2(2x)+600 (11-0 pl(a)= -0.0094²_0.4x+600. So now plio) = -0.009(8)?–0.4684+600 PI (8) = 596.224 | Pl (8) = 8596.22 Aue

d) so now we know that formula : P(x) = plast pllal (x-a). So now let above formua becomes Pla= P(8)+ p'L8) (R-8) so now pla)=pl&lt ples) (9-89 P19) = P18)+ plis P(q) = 3985.66 +596.22 pla)= 4,581-88 1219)= $ 4581-58| Tue