Faustina Chemical Corporation manufactures three chemicals (TX14, NJ35, and KS63) from a joint process. The three chemicals are in industrial grade form at the split-off point. They can either be sold at that point or processed further into premium grade. Costs related to each batch of this chemical process is as follows: TX14 N335 KS63
Sales value at split-off point $16,000 $12,000 $5,000
Allocated joint costs $ 6,000 $ 6,000 $6,000
Sales value after further processing$20,000 $18,000 $9,000
Cost of further processing $5,000 $ 3,000 $2,000
For which product(s) above would it be more profitable for Faustina to sell at the split-off point rather than process further?

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?