Ace Novelty wished to produce two types of souvenirs: type A and type B. Each type A souvenir will result in a profit of $1, and each type B souvenir will result in a profit of $1.20. To manufacture a type A souvenir requires 2 minutes on machine I and 1 minute on machine II. Type B souvenir requires 1 minute on machine I and 3 minutes on machine II. There are 180 minutes available on machine I and 300 minutes available on machine II for processing the order. How many souvenirs of each type should Ace make in order to maximize profits

The monthly demand equation for an electric utility company is estimated to be p equals 60 minus left parenthesis 10 superscript negative 5 baseline right parenthesis x, where p is measured in dollars and x is measured in thousands of killowatt-hours. the utility has fixed costs of $3 comma 000 comma 000 per month and variable costs of $32 per 1000 kilowatt-hours of electricity generated, so the cost function is upper c left parenthesis x right parenthesis equals 3 times 10 superscript 6 baseline plus 32 x. (a) find the value of x and the corresponding price for 1000 kilowatt-hours that maximize the utility's profit. (b) suppose that the rising fuel costs increase the utility's variable costs from $32 to $38, so its new cost function is upper c 1 left parenthesis x right parenthesis equals 3 times 10 superscript 6 baseline plus 38 x. should the utility pass all this increase of $6 per thousand kilowatt-hours on to the consumers?