# Thread: Mathematical Models (Price, Revenue, Profit)

Assume that the linear cost and revenue models apply. An item costs $13 to make. If fixed costs are$2500 and profits are $300 when 200 items are made and sold, find the revenue equation. (Let x be the number of items.) 2. ## Re: Mathematical Models (Price, Revenue, Profit) Does anyone know how to solve this without knowing the revenue component to the profit equation? Can't seem to figure it out. Thanks in advance! 3. ## Re: Mathematical Models (Price, Revenue, Profit) Assume that the linear cost and revenue models apply. So the cost is of the form c= ax+ b and the revenue is of the form r= dx+ e where x is the number of items mad and sold. That is what "linear" means- the graph of y= ax+ b is a straight line no matter what a and b are. An item costs$13 to make. If fixed costs are $2500 and profits are$300 when 200 items are made and sold, find the revenue equation. (Let x be the number of items.)
The "fixed costs" are what we have to pay even if we produce 0 (cost of building, etc.). if x= 0, c= a(0)= b= b so b= $2500. "An item costs$13 to make". So to make 1 we would add 13(1) to the fixed costs, if we make 32 we would add 13(2) to the fixed cost, etc. If we make "x" we add 13x to the fixed costs: c= 13x+ 2500. We clearly won't make any money if we don't sell anything so there is no "fixed" profit! e= 0. So the revenue, when we sell x items is r= dx. Profits are "revenue- costs so dx- 13x+ 2500. "Profits are \$300 when 200 items are made and sold" so d(200)- 13(200)+ 2500= 300. Solve that equation for d.

(Most of the terms here, "cost", "revenue", "profit", are from economics or business admin, not mathematics.)