Respuesta :
Answer:
the revenue function is R(Q)=$55/swshrt * Q and the profit function is P(Q)=$3496 - $38/swshrt * Q
Explanation:
since the cost function is linear , then denoting C as cost , Q as quantities of sweatshirts and 1 and 2 as reference points , we get
C= C₁ + (C₂-C₁)/(Q₂-Q₁)*(Q-Q₁)
replacing values
C= $4346 + ($7576- $4346)/(240 -50 )*(Q-50 )= $4346 + $17/swshrt*(Q- 50)
and the revenue function (total sales is )
R= P*Q = $55/swshrt * Q
the profit function is therefore
P = R - C = $55/swshrt * Q - [$4346 + $17/swshrt*(Q- 50)] = $3496 - $38/swshrt * Q
Notes
- Revenue refers to the total income generated , while profit refers to the income after costs and expenses
- We can verify the cost equation for C . For Q=Q₁
C= C₁ + (C₂-C₁)/(Q₂-Q₁)*(Q₁-Q₁) = C₁ + 0 = C₁
and for Q=Q₂
C= C₁ + (C₂-C₁)/(Q₂-Q₁)*(Q₂-Q₁) = C₁ + C₂-C₁ = C₂
thus our equation is correct
Answer:
The revenue equation is TR=55*P
Total cost equation is TC=3496+17Q
Explanation:
The formula for revenue is given quantity multiplied by price
TR=PQ
P is the price per unit ]
Q is the total quantity
since P is $55
TR=55P
The total cost function can also be determined thus:
TC =a+bQ
where a is the fixed cost
b is variable cost per unit
Q is the number of output
when TC is $4346,Q was 50
when TC was $7576 Q was 240
7576=a+240b
4346=a+50b
subtracting the two equations
3230 =190b
b=3230/190
b=$17
by substituting b in any of the equations,fixed cost can be determined
4346=a+(17*50)
4346=a+850
a=4346-850
a=3496
Total cost function
TC=3496+17Q
