Problem: The marketing department of Spager Ltd estimated that if the selling price of product is set at $15 per unit then the sales will be 50 units per week, while, if the selling price is set at $20 per unit, the sales will be 30 units per week. Assume that the graph of this function is linear. The production department estimates that the variable cost will be $5 per unit and that the fixed cost will be $50 per week, and special cost are estimated as $0.125x2, where x is the quantity of output. All production is sold.
Required:
- Show that the relationship between price (Pr) and quantity sold (x) , are given by the equation Pr = 27.5 - 0.25x.
- Find the revenue function, R.
- Find the total cost function (C).
- Advise the company on production and pricing policy if it wishes to maximize profits, and find the maximum profit.