Britte-lite Electric Company produces two types of electric lightbulbs; a 100-watt bulb and a 3-way (50–100–150) bulb. The machine that produces the bulbs is fairly old. Due to higher maintenance costs and down time, the contribution per unit for each additional unit produced decreases as the machine is used more intensely. Britte-lite has fit the following functions to per-unit contribution (in $) for the two types of lightbulbs it produces:
The Britte-lite Company is in the unusual position of being able to determine the number of units demanded of a particular type of lightbulb from the amount (in $) it spends on advertisements for that particular bulb.
where y1 is the amount (in $) spent on advertisements for 100-watt bulbs, and y2 is the amount (in $) spent on advertisements for 3-way bulbs
. Britte-lite has an advertising budget of $1500. Its management is committed to meeting demand. Present production capacity is 125 and 175 units of 100-watt and 3-way bulbs, respectively. Finally, the production of a unit of lightbulb j consumes ai j units of resource i for i = 1, 2, . . . , m, of which only bi units are available.