Answer: The company should produce 7 skateboards and 16 rollerskates in order to maximize profit.
Step-by-step explanation: Let the skateboards be represented by s and the rollerskates be represented by r. The available amount of labour is 30 units, and to produce a skateboard requires 2 units of labor while to produce a rollerskate requires 1 unit. This can be expressed as follows;
2s + r = 30 ------(1)
Also there are 40 units of materials available, and to produce a skateboard requires 1 unit while a rollerskate requires 2 units. This too can be expressed as follows;
s + 2r = 40 ------(2)
With the pair of simultaneous equations we can now solve for both variables by using the substitution method as follows;
In equation (1), let r = 30 - 2s
Substitute for r into equation (2)
s + 2(30 - 2s) = 40
s + 60 - 4s = 40
Collect like terms,
s - 4s = 40 - 60
-3s = -20
Divide both sides of the equation by -3
s = 6.67
(Rounded up to the nearest whole number, s = 7)
Substitute for the value of s into equation (1)
2s + r = 30
2(7) + r = 30
14 + r = 30
Subtract 14 from both sides of the equation
r = 16
Therefore in order to maximize profit, the company should produce 7 skateboards and 16 rollerskates.
Q55.
UTA+ATS=UTS
x+18+120=12x+17
x+138=12x+17
12x-x=138-17
11x=121
x=121/11
x=11
mUTA=x+18
put the value of x
11+18
mUTA=29
Q57.
AQP+RQA=RQP
9x+2+75=1+28x
9x+77=1+28x
28x-9x=77-1
19x=76
x=76/19
x=4
mRQP=1+28x
put the value of x
1+28(4)
1+112
mRQP=113
