Acompany produces two products, a and b. the sales volume for a is at least 80% of the total sales of both a and b. however, the company cannot sell more than 110 units of a per day. both products use one raw material, of which the maximum daily availability is 300 lb. the usage rates of the raw material are 2 lb per unit of a, and 4 lb per unit of b the profit units for a and b are $40 and $90, respectively. determine the optimal product mix for the company

The management of a supermarket wants to adopt a new promotional policy of giving a free gift to every customer who spends more than a certain amount per visit at this supermarket. the expectation of the management is that after this promotional policy is advertised, the expenditures for all customers at this supermarket will be normally distributed with a mean of $95 and a standard deviation of $20. if the management wants to give free gifts to at most 10% of the customers, what should the amount be above which a customer would receive a free gift?