i have project past due because i can not figure it out this

i have project past due because i can not figure it out! this is all it says Goal Use Quadratic Equations Role You are the vice president of production in the Fly By Night Company. Audience The other VP\'s in the executive meeting Situation You must make a report to the other executives about the monthly production (P) cost and revenue cost. When the revenue (R) cost equals the production cost the company breaks even. You have defined production cost as P = 8x + 4. The revenue cost is 8R - 3x2 = 0. The variable x in both equations is the number of units in thousands of its product manufactured and sold per month. Performance The student will make an analysis about the situation above. In the proposal there will be a chart showing what it costs to produce x = 1, 4, 10 units (remember x is in thousands). There should be a chart showing the income from x = 1, 4, 10 units. Analyze for the executives what is happening in each of the x values. Find the \"break even\" value for x. Also answer the question that was proposed by Mr. Slate, \" How many units should be produced to make a profit of $3,000?\" Standard The student will check the rubric to see what is expected. The student will meet the above requirements in a presentation that is easy to understand. There will be a summative paragraph of 4 sentences written explaining what was done in the project.

Solution

Production cost : P = 8x +4

Revenue : R = 3x^2/8

Chart of production cost :

x= 1 ; R = 3(1)^2/8 = 3/8 = 375 unit

x=4 ; R = 3(4^2)/8 = 6 = 6000 units

x=10 ; R = 3(10^2)/8 = 37.5 = 37500 units

Breakeven values : 8x +4 =3x^2/8

64x +32 = 3x^2

3x^2 -64x -32 =0

Apply to quadratic formula : we get x = 21.82 thousand = 21820

Profit = $3000

Profit = R - P = 3x^2/8 - 8x -4

3000 =3x^2/8 -8x -3

24000 = 3x^2 - 64x -24

3x^2 -64x -24024 =0

Use quadratic 3x^2 -64x -24024 =0

neglecting -ve root . x= 100.78 thousand