A company distributes college logo sweatshirts and sells them for $50 each. The total cost function is linear, and the total cost for 90 sweatshirts is $3564, whereas the total cost for 260 sweatshirts is $5944.(a) Write the equation for the revenue function R(x)
(b) Write the equation for the total cost function
(c) Find the break-even quantity. sweatshirts

The total revenue equation is TR=50Q

The total cost equation TC=2304+14Q

Equilibrium quantity is 64

Step-by-step explanation:

The total cost function can be written TC=a+bQ, where TC is the total cost ,a fixed cost ,b is the variable cost per unit and Q the quantity produced

Revenue function can be given TR=P*Q, where TR is total revenue,P is the price per unit and Q quantity sold

since P is $50

TR=50P

when TC=$3564,

3564=a+90Q equation 1

when TC=$5944

5944=a+260bequation 2

Solving simultaneously,we subtract equation 1 from 2

5944=a+260b

3564=a+90b

2380=170b

b=2380/170

b=$14

We substitute for b in any of the equations

3564=a+(14*90)

3564=a+1260

a=3564-1260

a=2304

Hence the total cost equation is

TC=2304+14Q

At equilibrium TC =TR

50P=2304+14Q

50P-14Q=2304

36Q=2304

Q=64

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now keep you pencil there and go up however many times it says on y(if it is positive) if it is negative then go down however many times it says. if it says 0 go nowhere.

you have just plotted a point! now when you finish plotting all of them connect them with a ruler

plot each point as (-3, 7), (0,4), (3,1), (8,-4)   in the parenthesis on the left of the comma is x and the right is y.

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step-by-step explanation: