Sport Tee Corporation manufactures T-shirts bearing the logos of professional football teams. The wholesale market for sport T-shirts is perfectly competitive. The manager forecasts the wholesale price of T-shirts next year to be $7.00. The firm's estimated marginal cost is where Q is the number of T-shirts produced and sold each month. Sport Tee Corporation will have a fixed cost of $2,000 per month.
- Given the estimated marginal cost function above, write the equation for the average variable cost function and the total variable cost function.
- What is the profit-maximizing number of T-shirts that Sport Tee should produce and sell each month? (Note: you will find 2 output levels that are solutions to your optimization problem. Test which one is actually the optimal level of output).
- How much monthly profit (or loss) will Sport Tee Corporation earn?