Quantitative Methods Homework - 3300 Words

Quantitative Methods Homework (Math Problem Sample) Content: STUDENTS NAME:NAME OF THE UNIT:INSTITUTION:DUE DATE:1.(a)Tc=Fc+VcTc=total cost65000+(7.5*15000)=177,500Tr=total revenueTr=25*15,000=37,500Profit=Tr-Tc375,000-177,500=197,500Therefore profit is $197,500 1 (b)q=fc/(Up-Vc)Whereq=break even volumeFc=fixed costVc= variable cost per unitUp=unit priceThereforeq=65,000/(25-7.5)=3,714 units 2 q=fc/(Up-Vc)25,000/(0.45-0.25)25,000/0.25100,000 units 3 The fixed cost remains the same even after changing the price=$25,000Variable cost=$0.20Unit price=$0.55q=fc/(Up-Vc)25,000/(0.55-0.20)25,000/0.35=71,428Therefore changing the price decreases the break even volume by 28,572. 4 Advertising expenditure will increase the fixed costAdvertising cost per month=10,000/12=833.33Fixed cost=25,000+833.33=25,833.33q=fc/(Up-Vc)25,833.33/(0.45-0.20)25,833.33/0.25=103,333.33Advertising expenditure will increase the break even volume by 3,333.33 units 5 Fixed cost=$3,000+$3,500=$6,500Varied cost=0.40Break even point=1,500*6=9,000q=fc/(Up-Vc)9,000=6 ,500/(Up-0.40)9,000(Up-0.40)=6,5009,000Up-3,600=6,5009,000Up=10,100Up=1.125Therefore she needs to charge $1.125 for a hotdog in order to break even5.(b.) factors that would alter the volume sold * Changes in the cost of a hot dog * Attendance may not be as predicted in all games 6 (A)Initial start up cost=$400,000Tuition fee=$20,000 per yearThe college is also required to pay $10,000 per student for the first 100 students to the administrationq=fc/(Up-Vc)q=400,000/(20,000-10,000)400,000/10,000=40=40 students6 (B)Profits=revenue-costsRevenue=80*20,000=1,600,000Cost=400,000+(80*10,000)à ¢Ã¢â€š ¬Ãƒ ¢Ã¢â€š ¬..since the 1st 100 students are to cost the college$10,000 eachCost=1,200,000Profit=1,600,000-1,200,000=$400,0006 (c)The college has to consider whether increasing the tuition fee will bring in profit higher than the current $ 400,000 (calculated in 6 (B) above)Profit=revenue-costRevenue=25,000*50=1.250,000Cost=400,000+ (50*10,000)=900,000Profit=1,250,000-900,000Profit=350,000There fore the college should not consider increasing the tuition fee as the profit would decrease by $50,000. 7 Grade A B C D F Probability 0.1 0.2 0.4 0.2 0.10 Scale 4 3 2 1 0 Ex=x1p1+x2p2+à ¢Ã¢â€š ¬Where E(x)=the expected gradeX1=value of grade 1p1=probability of grade 1thereforeE(x)=(0.1*4)+(0.2*3)+(0.4*2)+(0.2*1)+(0.10*0)=0.40+0.6+0.8+0.2+0=2Therefore the expected grade is C7(B)To calculate the variance: * Find the mean (average of the Numbers) * For each number, subtract the mean square the results (to get the squared difference) * Work out the average of the squared differenceStep I. mean=expected grade=2 (calculated in 7 (a)Step ii getting the squared difference4-2=22=43-2=12=12-2=02=0 Quantitative Methods Homework - 3300 Words Quantitative Methods Homework (Math Problem Sample) Content: STUDENTS NAME:NAME OF THE UNIT:INSTITUTION:DUE DATE:1.(a)Tc=Fc+VcTc=total cost65000+(7.5*15000)=177,500Tr=total revenueTr=25*15,000=37,500Profit=Tr-Tc375,000-177,500=197,500Therefore profit is $197,500 1 (b)q=fc/(Up-Vc)Whereq=break even volumeFc=fixed costVc= variable cost per unitUp=unit priceThereforeq=65,000/(25-7.5)=3,714 units 2 q=fc/(Up-Vc)25,000/(0.45-0.25)25,000/0.25100,000 units 3 The fixed cost remains the same even after changing the price=$25,000Variable cost=$0.20Unit price=$0.55q=fc/(Up-Vc)25,000/(0.55-0.20)25,000/0.35=71,428Therefore changing the price decreases the break even volume by 28,572. 4 Advertising expenditure will increase the fixed costAdvertising cost per month=10,000/12=833.33Fixed cost=25,000+833.33=25,833.33q=fc/(Up-Vc)25,833.33/(0.45-0.20)25,833.33/0.25=103,333.33Advertising expenditure will increase the break even volume by 3,333.33 units 5 Fixed cost=$3,000+$3,500=$6,500Varied cost=0.40Break even point=1,500*6=9,000q=fc/(Up-Vc)9,000=6 ,500/(Up-0.40)9,000(Up-0.40)=6,5009,000Up-3,600=6,5009,000Up=10,100Up=1.125Therefore she needs to charge $1.125 for a hotdog in order to break even5.(b.) factors that would alter the volume sold * Changes in the cost of a hot dog * Attendance may not be as predicted in all games 6 (A)Initial start up cost=$400,000Tuition fee=$20,000 per yearThe college is also required to pay $10,000 per student for the first 100 students to the administrationq=fc/(Up-Vc)q=400,000/(20,000-10,000)400,000/10,000=40=40 students6 (B)Profits=revenue-costsRevenue=80*20,000=1,600,000Cost=400,000+(80*10,000)à ¢Ã¢â€š ¬Ãƒ ¢Ã¢â€š ¬..since the 1st 100 students are to cost the college$10,000 eachCost=1,200,000Profit=1,600,000-1,200,000=$400,0006 (c)The college has to consider whether increasing the tuition fee will bring in profit higher than the current $ 400,000 (calculated in 6 (B) above)Profit=revenue-costRevenue=25,000*50=1.250,000Cost=400,000+ (50*10,000)=900,000Profit=1,250,000-900,000Profit=350,000There fore the college should not consider increasing the tuition fee as the profit would decrease by $50,000. 7 Grade A B C D F Probability 0.1 0.2 0.4 0.2 0.10 Scale 4 3 2 1 0 Ex=x1p1+x2p2+à ¢Ã¢â€š ¬Where E(x)=the expected gradeX1=value of grade 1p1=probability of grade 1thereforeE(x)=(0.1*4)+(0.2*3)+(0.4*2)+(0.2*1)+(0.10*0)=0.40+0.6+0.8+0.2+0=2Therefore the expected grade is C7(B)To calculate the variance: * Find the mean (average of the Numbers) * For each number, subtract the mean square the results (to get the squared difference) * Work out the average of the squared differenceStep I. mean=expected grade=2 (calculated in 7 (a)Step ii getting the squared difference4-2=22=43-2=12=12-2=02=0