Omkara, a furniture manufacturer, contracts with foam gnome for $50,000 worth of foam, which omkara will use for making ten sofas she has agreed to make for duke's furniture. a day before gnome is going to ship the foam to omkara, a flood destroys its entire inventory. gnome tells omkara it cannot send her the foam in time, but tells her that firmfoam can supply her with an identical shipment for $65,000. this increase in price will wipe out twenty percent of omkara's profit from her contract with duke's. omkara wants to get out of both contracts. can she?

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?