Question

Date Assigned: Monday, June 22, 2020 Date Due: Tuesday, June 23, 2020 before class, No late homework will be accepted. Homework 15 Please notice that all work must be shown in a professional way with attention to detail No credit will be given for incomplete or disorderly work Please use a cover sheet stating your name, course number, date due, and homework number Unstopled homework will not be collected as this is part of the assignment All work must be individual with emphasis on numerical accuracy This is an Excel based assignment that must be submitted following the stated guidelines Please notice that late homework (after collected by the instructor) will incur into a 25% fate fee 1. Exercise One: Van Dam Design produces a line of high end sunglasses. The cost of production for this model is given by the function C(x) shown below-where x is the production volume in units. In addition, if the sunglasses sell for $520 per unit, the revenue function R(x) is shown below - where x is the sales volume in units. C(x) = 25,000 + 20 x R(x) = 520 x Based on the given information: (a) Derive the total profit function, (b) as shown in class, graph the Cost function C(x), and the Revenue function R(x) on the same Cartesian plane. (c) Find the break-even point numerically by using Goal Seek as shown in class. 2. Exercise Two: CDP plastics produces a line of economical, sun powered pocket calculators. The cost of production for this model is given by the function Clx) shown below-where x is the production volume in units. In addition, if the sunglasses sell for $10 per unit, the revenue function R(x) is shown below-where x is the sales volume in units. Cix) = 2x + 8000 R(x) = 10 x Based on the given information: (a) As shown in class today, derive the total profit function, (b) on the same Cartesian plane, graph the Cost function Clx), and the Revenue function R(x). (c) Find the break-even point numerically by using Goal Seek as shown in class.

Answer 1

X SOLUTION 1:- Total Profit = Total Revenue-Total Cots Therefore, Profit function '=Revenue Function-Cost Function =520X-(25000+20%) =520X-25000-20X =500X-25000 Cost Revenue Profit/(Loss) 10 = 25000+(20*10) =520*10 =5200-25200 25200.00 5200 -20,000 Revenue, Cost and Profit(Loss) Qty Cost 60000 50000 40000 30000 10 20 20000 Break Even is a point where, Total Revenue =Total Cost 30 10000 40 Break Even Point is 50 Revenue Profit/(Loss) 25200 5200 -20000 25400 10400 - 15000 25600 15600 -10000 25800 20800 -5000 26000 26000 0 Break Even 26200 31200 5000 26400 36400 10000 26600 41600 15000 26800 46800 20000 27000 52000 25000 0 -10000 1 2 3 4 5 6 7 8 9 10 520X=25000+20X 500X=25000 X=25000/500 X=50 60 70 -20000 80 -30000 90 Qty Cost Revenue Profit/(Loss) So Break even will be when 50 Quantities are actually sold. 100 rolTION

X SOLUTION 2:- Total Profit = Total Revenue-Total Cots Therefore, Profit function =Revenue Function-Cost Function =10X-2X+8000) =8X-8000 Cost Revenue Profit/(Loss) 100 = (2*100)+8000 *=10*100 =1000-8200 8200.00 1000 -7,200 Revenue, Cost and Profit(Loss) 25000 Qty 20000 Cost 200 400 600 15000 8800 Break Even is a point where, Total Revenue =Total Cost 10000 800 5000 Break Even Point is 1000 Revenue Profit/(Loss) 8400 2000 -6400 4000 -4800 9200 6000 -3200 9600 8000 -1600 10000 10000 0 10400 1600 Break Even 10800 14000 3200 11200 16000 4800 11600 18000 6400 12000 20000 8000 0 1200 10X=2X+8000 8X=8000 X=8000/8 X=1000 12000 1 2 3 4 5 6 7 8 9 10 1400 -5000 1600 -10000 1800 So Break even will be when 1000 Quantities are actually sold. Cost Qty 2000 Revenue -Profit/(Loss)