As sales manager for Montevideo Productions, Inc., you are planning to review the prices you charge clients for television advertisement development. You currently charge each client an hourly development fee of $2,500. With this pricing structure, the demand, measured by the number of contracts Montevideo signs per month, is 15 contracts. This is down 5 contracts from the figure last year, when your company charged only $2,000.

• Construct a linear demand equation in the form q= ap + b where the number of contracts q is given as a function of the hourly fee p Montevideo charges for development.
• Give a formula for the total revenue obtained by charging $p per hour.
• The costs to Montevideo Productions are estimated as follows: Fixed costs: $120,000 per month and Variable costs: $80,000 per contract. Express Montevideo Productions’ monthly cost as a function of the hourly production charge p.
• Express Montevideo Productions’ monthly profit as a function of the hourly development fee p and hence the price it should charge to maximize the profit.

The XYZ Clothing Company manufactures football boots for sale to College/University bookstores, in Trinidad. Football boots are in runs of up to 500. It cost (in dollars) for a run of x football boots is:

𝐶(𝑥) = 3,000 + 8𝑥 + 0.1𝑥2 0 ≤ 𝑥 ≤ 500

XYZ Clothing sells the football boots at $ 120 each.

(a) How many football boots does XYZ have to sell to breakeven?

(b) How many football boots does XZY have to sell to make maximum profit?

(c) On a labelled pair of axes, sketch the XYZ’s profit function. Label all important points.