Answer:
(i) The cost function is C(q) =5q + 400
(ii) The profit function =for weekly profit
(iii) the maximum profit is $243.75
Step-by-step explanation:
(i) the cost function will be C(q) = FC(q) + V(q)
fixed costs FC(q) as a function of quantiyy and variable costs VC(q) we already know that the fixed cost is the $400 per week from charges to use facilities then Variable costs is $5 times the quantity of t shirts sold per week.
so C(q) = $400 + 5q
(ii) The profit function will be found by multiplying quantity demanded with the price at which that quantity is demanded at so we have a demand function q= -4p + 200 then we make the price the subject of the formula
p = 200/4 - q/4 we divided both sides by 4 after transposing -4p
then we get p= 50 - q/4 which is the price of the quantity demanded then we multiply this price by q
thereafter we get pq = 50q - q^2 /4
which is our profit function because p x q is revenue/ profit ;