The total cost is calculated as:

• TC=FC+VCTC=FC+VC

Given the total cost function:

• TC=0.5Q2+25Q+1,000TC=0.5Q2+25Q+1,000

The fixed cost will be determined when Q = 0.

• FC=TC(0)=1,000FC=TC(0)=1,000

Therefore, the variable cost will be equal to:

• VC=TC−FC=0.5Q2+25Q+1,000=1000=0.5Q2+25QVC=TC−FC=0.5Q2+25Q+1,000=1000=0.5Q2+25Q

The variable cost of catering to Q = 30 birthday parties is equal to:

• VC=0.5(30)2+25(30)=$1,200VC=0.5(30)2+25(30)=$1,200

Thus, the average variable cost of catering for 30 birthday parties is equal to:

• AVC=VCQ=120030=$40AVC=VCQ=120030=$40 per birthday party.