mathematics in business

Question 1 Determine the slope for line 2x+12y-6=0
2x+12y=6
12y=-2x+6 y=-2x/12+6/12 y=-x/6+1/2
∴m=-1/6
Find the slope of the required line, which is "m"
(-1/6)("m" )=-1 (m)=6 Now, substitute m=6 into equation y=mx+c ,i.e. y=6x+c.
This line passed through point (2,4). So, we substitute x=2,y=4 into y=6x+c. 4=6(2)+c
4-12=c
c=-8
∴ The equation of the straight line that we are looking for is y=6x-8

y=3x^2-11x+6, where a=3,b=-11,c=6.
The quadratic formula: x=(-b±√(b^2-4ac))/2a x=(-(-11)±√(〖(-11)〗^2-4(3)(6)))/(2(3)) x=(11±√(121-72))/6 x=(11±√49)/6 x=(11±7)/6 x=(11+7)/6 x=18/6 x=3 x=(11-7)/6 x=4/6 x=2/3
∴ x=3 ,2/3

Question 2 Total revenue = (Unit Price) x (Total quantity sold)
Product X :
=400q
Product Y :
=500q
Total Cost = Variable costs + Fixed costs
Product X :
=50q+2000
Product Y :
=80q+1000
Total Profit = Total Revenue – Total Costs
Product X :
=400q-(50q+2000)
=400q-50q-2000
=350q-2000
Product Y :
=500q-(80q+1000)
=500q-80q-1000
=420q-1000
Break-even point in RM and units
Total Revenue = Total Cost
Product X : 400q=50q+2000
400q-50q=2000
350q=2000 q=2000/350 q=5.7143

∴ To find break-even point in RM, price per units × units :
=50×5.5143
=RM275.72
Hence, 5.5143 units and RM 275.72 .
Product Y : 500q=80q+1000
500q-80q=1000
420q=1000 q=1000/420 q=2.381
∴ To find break-even point in RM, price per units × units :
=80×2.381
=RM190.40
Hence, 2.381 units and RM 190.40 . Unit to be sold if profit of RM 1000 is targeted
Product X :
Substitute q=1000 into 350q-2000
Profit =350(1000)-2000 =350000-2000 =348000
Product Y :
Substitute q=1000 into 420q-1000
Profit =420(1000)-1000 =420000-1000